Christian Ziege's superb strike after only eight minutes nullified the chances of an FA Cup upset, but Watson was happy with the way his side kept plugging away against Premiership opponents.
"We had a lot of chances without tucking any away," said Watson. "To give a goal away after only eight minutes was always going to make it difficult for us.
"But, in saying that, I thought our lads kept going and even late on in the second half we were still creating one or two chances.
"I think if you come and sit back here Tottenham are always going to get a chance - they proved that after the eight minutes when they got the goal. I thought after that we stuck at it and kept trying to get back into the game.
"If you make mistakes against the likes of your Tottenhams, if you give them a chance they'll tuck it away and that's what they done today.
"From set pieces we gave them one or two problems and we should have got a couple of goals from them."
Watson was asked if he had any complaints about our third goal from Teddy Sheringham where Les Ferdinand tangled with keeper John Achterberg.
"In that situation you expect your keeper to take the ball and the man and stop it. I'd have to see it again, sometimes you get them, sometimes you don't and we never got that today. But I would certainly have expected my keeper to flatten the lad and get the ball there.
"They played well, they are a Premiership team and have got quality right through the side. We were under no illusions coming here, thinking it was going to be easy. Tottenham are an excellent footballing side and they showed that in patches today.
"But I was just proud of our lads the way they stuck at it and kept trying to get back in the game."
Tranmere boss Dave Watson reflected that it was always going to be an uphill struggle for his side after conceding an early goal.