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.
Very early bath: Crouch (2nd left) is giving his marching orders in Madrid
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.'
World class: Di Maria (floor) celebrates scoring Madrid's third
Adebayor's second and strikes from Angel Di Maria and Cristiano Ronaldo sealed the victory for Jose Mourinho's men, and Dawson admitted that he and his team-mates had little chance of staying in the game after Crouch's dismissal.
'Going down to 10 against Real Madrid is always going to be hard.
'After conceding the second, it was an uphill battle and the last two goals were world class finishes.'
Dawson still maintains that the Londoners have a chance of making the last semi-finals and has called on his team-mates to pick themselves up for Saturday's game against Stoke.
'We have to pick ourselves up again for Saturday and then we have the return leg at White Hart Lane.
'There's 90 minutes of the tie left to play. We will go there, give it our all and see where it takes us,' added the Tottenham defender.
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Source: Daily Mail
Source: Daily Mail