With Spurs already 1-0 down thanks to Emmanuel Adebayor's opener, the England striker saw red after just 15 minutes for two needless fouls on Marcelo and Sergio Ramos.
Without him, Tottenham struggled and Jose Mourinho's men ran riot, taking the first leg of their Champions League quarter-final with a 4-0 hammering.
Crouch refused to speak after the game at the Santiago Bernabeu, but Spurs skipper 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 (Crouch) 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."
Source: PA
Source: PA