The Reds went ahead early before Milan made it 2-1 with two goals just before half-time.
However, Jurgen Klopp's side fought back to secure all three points thanks to second-half goals from Mohamed Salah and Jordan Henderson.
"I would say the result in the first half (Milan went into the interval 2-1 up) was a liar for what Liverpool had shown," former England boss Capello said on Sky Italia.
"I think this can be a great lesson for Milan to understand the level of the Champions League. Great-quality players, great rhythm, great pressing – you can't play at a slow pace.
"Milan lost possession because the ball came too slowly. The great speed and determination of this (Liverpool) team created problems."
"There was no worse return to the Champions League than Liverpool, given this crowd and this atmosphere.
"Too bad for the goal at the beginning of the second half, because the stadium was quieter than usual."
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