Bayern were already 3-0 ahead when Alonso caught Robert Lewandowski with his arm in the 82nd minute, a challenge he initially saw a yellow card for.
However, after a check of the VAR monitor, the referee upgraded his decision to a red card, meaning Alonso will miss the return leg at the Allianz.
"He's let his manage down there no doubt," said Cole. "It looked like [Alonso and Lewandowski] said something to each other so there was a bit of malice, bit of venom. He shouldn't have done that and he's let the team down."
Jorginho is also ruled out of the round 16 second leg through suspension after picking up a yellow card for dissent during Tuesday night's game.