The Bundesliga side blitzed their way past the reigning champions 5-2 on Tuesday night in their quarter-final first leg at San Siro.
And Rangnick has said he learned a few things beforehand from Milan after watching last Saturday's derby della Madonnina, in which the Serie A leaders toppled the Nerazzurri 3-0.
"I did well to watch the Milan derby game at San Siro as I realised Inter couldn't press the midfield and they were leaving lots of space against Milan," he told Il Corriere dello Sport.
"They were vulnerable against fast players like Pato, leaving Milan to take control. I asked my players to give it their best and take advantage.
"And my offensive choices paid off."
Tenth-placed Schalke take on Wolfsburg in the Bundesliga on Saturday, before hosting Inter in Wednesday night's return leg.
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