We missed a hatful of chances as Nigel Quashie's header won it for the home side in the second half.
In an open, exciting first hour, both sides were guilty in front of goal with Paul Smith in the Saints' goal stopping everything that came his way.
Jermain Defoe, Mido, Michael Brown and Fredi Kanoute were denied with Smith's first save in the first minute and last three minutes from time.
"We should have had a draw," reflected Martin at St Mary's. "You would normally get two or three chances away from home but I can't remember us having such a lot of initiative, having the ball and creating chances without getting something out of the game.
"The main thing they did was to hit Crouch and that was a bit of a problem for us. You have to pressurise all the time so they don't have the chance to play the ball to him, but we didn't do that.
"We still had two one-on-ones with their keeper and other chances from Mido and Stephen Kelly. We should have scored.
"In the second half the lads did everything we wanted. We played well, created a couple of 100 per cent chances, Defoe one-on-ones, Kanoute and a couple of half-chances and you have to put them away.
"You also have to give credit to their goalkeeper, maybe he was lucky on occasions but he also made some terrific stops.
"Southampton are fighting for their lives and did well but we should have got something out of this game."
If you don't, Southampton are fighting for their lives and they did well. Jamie Redknapp played well in midfield but we should have got something out of this game.
"Jermain is one of the best finishers, everyone knows that. You also have to give credit to their goalkeeper, maybe he was lucky on occasions but he also made some terrific stops.
"We wanted at least a draw because although Southampton haven't won a lot lately, they haven't lost at home for something like 14 games, so that's not bad.
Although disappointed, Martin Jol insisted defeat at Southampton wasn't a big blow in terms of the overall picture in the Barclays Premiership.
A lot of that disappointment from the Head Coach and lads came from the knowledge that victory at St Mary's would have lifted us into sixth spot in the table on Saturday night.
As it stands we remain ninth but only four points off Liverpool in fifth.
"It's a disappointment but I don't think it's a big blow," said Martin. "We had a game in hand and it's still pretty exciting because I believe there are still about 10 teams competing for fifth or sixth spot.
"We knew it would be tough. Southampton have only lost twice at home so as their away record is poor, they know they have to do it at home. They are fighting for their lives and did well but we should have got something from the game.
"The lads did everything we asked of them in the second half but score. We had the chances and you have to put one away."
Midfielder Michael Carrick agreed with Martin. "We're not getting too down," said the midfielder. "We're disappointed about the result, but we are still in a decent position. It was a chance missed, but hopefully there will be a few more chances to push up before the end of the season that we will take."
Spurs boss Martin Jol lamented the failure to finish with at least a point after seeing his side create a hatful of chances - but acknowledged Smith's heroics had a part to play.
"We had two one-on-ones with their keeper in the first half and Mido also had an opportunity. We should have scored. In the second half my players did everything I wanted of them - except score," he said.
"Defoe was through on the keeper and Kanoute had a shot saved. You have to put those chances away. We should have got something out of the game - Jermain is normally one of the best finishers around.
"But you have to give credit to their keeper. Maybe he was lucky on occasion but he did make some terrific stops."
He added: "We knew how much Saints wanted to win. Their away record is one of the worst in the league, so they know they have to do it at home. They were fighting for their lives.
"But I'm pleased for Jamie Redknapp. I thought he had a great game. He left Tottenham to help his dad and I don't begrudge either of them today's victory."
Southampton boss Harry Redknapp believes his side will escape relegation from the Barclays Premiership after they edged past Tottenham 1-0 at St Mary's.
Crystal Palace's goalless draw with Manchester United means Saints are just two points and one place away from safety and Redknapp claims that ground will be made up over the coming weeks.
"I did think there are four teams in it but maybe one or two others could get sucked in. With nine matches left to go who knows what will happen," he said.
"Myself and the players genuinely believe we can stay up. Four or five weeks ago I thought we had no chance, but then the transfer window opened, we brought five players in and we look a different side.
"The new players have made a big difference to us. When I arrived I was thinking how am I going to get this team out of trouble? But we're a much better side now. We're in good form - the team is playing well and working hard.
"If I'd had this team at the start of the season I reckon we would have finished around 11th place."
Nigel Quashie nodded home a 51st-minute Mikael Nilsson cross to give Saints' Premiership survival bid a massive shot in the arm but it was an impressive display from Henri Camara which really caught the eye.
Redknapp said: "With his pace he's always a threat. He created some great chances and looked dangerous all afternoon. Maybe he should have stuck one away but he's been fantastic since he's come into the side."
The Saints boss also had a word of praise for goalkeeper Paul Smith - standing in for the injured Antti Niemi - who made a string of fine saves, especially in the second half when Jermain Defoe and Frederic Kanoute were denied.
"Paul gave a terrific performance and he's been marvellous for us," he said. "We lost Niemi who is as good as anything in the Premiership, so it makes you fear the worst when you pick a boy who has never been in the first team.
"But Paul has been absolutely fantastic. He's played so well that he's given me a dilemma for when Niemi returns. At least I know I don't have to rush Niemi back now."
It was a pulsating encounter which saw plenty of action at both ends and Redknapp admitted he was a nervous spectator in the closing stages as Spurs poured forward in search of the equaliser.
He said: "It was tense at the end. To me the best feeling in the world is when you're 1-0 up and the referee blows that final whistle. It's an indescribable feeling. Maybe I need to get out more!"
Martin Jol was scratching his head after we ended goal-less and point-less at Southampton on Saturday.