Crouch was sent off in the 15th minute of the Champions League quarter-final first leg for two bookings when Spurs were 1-0 down and Madrid took full advantage of their numerical superiority.
''We go away disappointed, we've got to pick ourselves up because we've got to put in a performance next week,'' Dawson said on Sky Sports. ''After going down to 10 men early on it was so difficult.''
Tottenham, who conceded an early Emmanuel Adebayor goal, managed to keep the scoreline to 1-0 by half-time, but Madrid ran away with the match it the second half as Adebayor doubled his tally before Angel Di Maria and Cristiano Ronaldo also netted.
''We defended well after giving the early goal away, we got blocks in,'' added Dawson. ''To give another goal away was disappointing and then they scored two top-class goals.
''The White Hart Lane faithful will be there next Wednesday and we've got to go out and give it our all.''
Redknapp admitted everything had gone wrong for Tottenham, who had to change their team at the last minute, bringing in Jermaine Jenas for the ill Aaron Lennon.
''We lost Aaron Lennon a minute before kick-off, he didn't feel well, just said he had no energy, no strength. We had to change the team just as we were leaving the dressing room,'' he said.
''Then we went a goal down and got Crouchy sent off. 'It's difficult to come here with 11 men let alone to come and play with 10.''
On the sending off, Redknapp said: ''He's certainly not one for getting red cards, but I've not seen it.'' He added: ''To get to half-time like we did, I thought we could hang in there and would have a chance, but then our legs ran out a bit.
''It was one of those days where anything that could have gone wrong did go wrong.'' Redknapp revealed Gareth Bale struggled with cramp in the second half and Vedran Corluka was forced off with an ankle problem.
Madrid boss Jose Mourinho admitted he felt sorry for Tottenham after Crouch's red card made their task nigh on impossible. ''I know at his level, 11 against 10, it's almost impossible,'' he said.
''It's just a question of the team with 11 keeping concentrated and we did that in the second half, not in the first half but in the second half we did that. 'For a team with 10 men for such a long time is an impossible mission. 'I feel sorry because with 11 against 11 the match would be much better.''
Mourinho said, though, Tottenham were still alive in the tie. He said: ''I know English football well, I know the English mentality. In another culture, yes, but with the English concept of football it's not over.''
Xabi Alonso insisted the tie was not over. ''Not even close,'' said. ''We have seen so many great comebacks. Hopefully this won't be the case, but we have to be ready.''
The Spain international added: ''We needed to be patient, we knew the chances would come. As soon as we scored the second one they were a little bit down. 'The result is fantastic but the tie is not won yet.''