Mido was dismissed by referee Rob Styles after an aerial challenge with Chelsea left-back Asier Del Horno in the 25th minute. Mido led with his arm as he went up for the ball but neverthless, a straight red card looked harsh.
The decision was all the more frustrating as minutes earlier, Edgar Davids was upended by Michael Essien as he burst through on goal but the Chelsea man was only handed a yellow card.
Del Horno went on to open the scoring with a header from a corner after 39 minutes before Damien Duff wrapped it up for the champions in the second half.
Head Coach Martin reflected: "I was very, very satisfied, maybe even proud after the first 25 minutes because I thought we did well.
"We knew beforehand that they could have a problem at White Hart Lane, we knew how to play against them and the first 25 minutes showed that.
"Then it was frustrating because we had to play with 10 men against 11.
"I don't think the red card was the right decision. Maybe Mido was a bit too enthusiastic, maybe it was a bit dangerous so you could have given him a yellow card, but instead it was a red card and straight off.
"Mido is still apologising to everyone and saying that he didn't do it with any intent.
"At 1-0 we still had a chance and even in the last 15 minutes we thought we had a chance but just when we made the decision to try something else (putting Michael Dawson up front) they scored a second goal.
"It was a frustrating afternoon for us but I'm proud of the lads because you can easily lose a game like this four or five-nil but we kept digging in when it was very difficult. It was just a shame because I felt we could do something out there."
Martin Jol was left frustrated by Mido's sending off but insisted he was proud of the lads after Saturday's 2-0 reverse against Chelsea.