Spurs were 1-0 up in the tie, when Allegri switched his system from a back three to a back four. Juventus took control of the game, scored two impressive goals, and rarely looked threatened at the back.
Former Tottenham manager Redknapp told talkSPORT: "Everyone is always ready to jump on the bandwagon, but what could Pochettino do?
"He's stood there and Tottenham are completely dominating the game.
"They went 1-0 up and were in complete control, Juventus were hanging on dear life. Suddenly in three minutes, you don't know how it's happened, but it's happened.
"I'm sure the Juventus manager couldn't see it coming either. When you're losing like that you have to make changes. They have used that system for years at Juve to great success, but it wasn't working for them last night.
"They were getting overrun, but suddenly you get a couple of breaks and the game has gone your way.
"I just think it was one of those things. Pochettino was stood there, his team were in control, Pochettino hasn't got to change anything, everything is going their way.
"But the goals changed the game completely. It's no different to the first leg – Juventus were 2-0 up and Tottenham came back. Did Allegri get out-coached by Pochettino there?"