Crouch was sent off after just 15 minutes of the quarter-final first leg at Real Madrid for a reckless challenge that brought a second yellow card.
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Real took full advantage, with former Arsenal striker Emmanuel Adebayor scoring twice and Angel Di Maria and Cristiano Ronaldo once each as Jose Mourinho's side completed a 4-0 rout.
Spurs boss Redknapp said: 'I knew it would be a difficult night but to lose a player after 15 minutes made it impossible. It was a case of trying to hang on. Even at 2-0 it would have been a miracle.
'I haven't seen a replay of the (second Crouch) tackle but I'm sure the referee made the right decision.
'He (Crouch) shouldn't have taken the chance he might get a red after having a yellow.
Early bath: Crouch was sent off after just 15 minutes for two bookable offences
'He's the most inoffensive footballer ever, isn't he? He's not one for getting red cards or making rash challenges. But he's lunged in for the second one and it's cost us dearly.
'It was impossible with 10 men. We've done it before this season on couple of occasions but to play that long against a good team was impossible for us.
'We did fantastically in the first half with 10 men but we ran out of steam.'
Tottenham also lost Aaron Lennon to illness just before kick-off, but Redknapp lay any blame on the winger.
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Redknapp said: 'He hadn't been feeling great and he had that look on his face. He said: "I don't feel I've got any strength, any energy." 'If he didn't feel fit there was nothing you can do.'
Captain Michael Dawson also admitted Spurs gave Madrid a 'helping hand' with Crouch's red card.
Dawson said: 'Going down to 10 men so early, it's hard work. They're good enough not to need a helping hand, but we gave them one.
'We defended well after giving the early goal away, but to give away another goal like we did was disappointing.'
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Real manager Jose Mourinho said: 'I feel complete sympathy (for Redknapp). I know how difficult it is to play in the Champions League with 10 men. It is like mission impossible. They will try everything in the second leg. White Hart Lane is a difficult place to go.
'I played in Barcelona with 10 players and you can only defend. This is a team that is known to be attacking but, with only 10 players, they couldn't really do much more.
'We fully deserved this score, but I feel sorry because I know the situation when a team plays with 10 players and they are unable to play the match they want to.'
Madrid will be without Pepe for the return leg after the central defender was booked last night.
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?Explore more:People: Cristiano Ronaldo, Michael Dawson, Peter Crouch, Harry Redknapp, Emmanuel Adebayor, Aaron Lennon, Jose Mourinho Places: Madrid, Barcelona
Source: Daily Mail
Source: Daily Mail