Crouch refused to speak after the game, but the Spurs captain Dawson said the striker had apologised for the error, which leaves the club with little hope of going through from next week's second leg.
"He was gutted," Dawson said. "He apologised to the lads but we went out there to give our all and it didn't go to plan. I didn't see the bookings so I don't know if they were harsh.
"To have it happen so early on when you are playing a team like Real Madrid was disappointing."