Milan lost 1-0 on aggregate after losing the first leg to a goal from Peter Crouch, but dominated the second game at White Hart Lane and were unfortunate not to score.
Allegri said: “The team put in a fine performance tonight and I think over the two legs we deserved to go through. Unfortunately, that mistake in the first leg cost us dearly. This evening my Milan did everything it possibly could, showing intensity and technique. We only lacked something in the finishing.”