Goals from Gus Poyet and Les Ferdinand capped a dominant display at Highfield Road and booked a home tie against Bolton in the fourth round.
Nilsson reflected: "We gave them a bit too much respect.
"When you are playing at home in a game like this, and want to get something from it, you have to take things to them and not let them dictate how the game is played.
"We didn't do that and once they scored the opening goal it was hard for us to get back into it.
"Tottenham showed what they can do in the Premiership every week but, unlike against Wolves on Sunday, I couldn't criticise our willingness to work hard and to try something.
"But I just felt we were hoping to get something from the game instead of going flat out at Tottenham."
Asked if we looked capable of going a long way in the competition, Nilsson added: "I'm sure they can. They had a few players out and the players who came in showed they are quality players. When they get those players back they will be even stronger."
Roland Nilsson had no complaints after our 2-0 FA Cup win at Coventry - only that his side gave us too much respect.