The Spanish side had several chances to score and had two penalty appeals turned down, but will return home with a result that leaves the quarter-final tie wide open for the return leg at Camp Nou next Tuesday.
"In the first few minutes we had some problems, but after that we did well," Xavi told reporters after the match.
"We had a great match and we dominated. We had several chances to score. We were unable to score, but we deserved to win.
"There was also a penalty in our favour. Christian Abbiati's foul on Alexis Sanchez was clear."
Meanwhile, Javier Mascherano refused to comment on Milan's approach to the game, but criticised the poor turf at San Siro.
"A defensive Milan? Everyone does what is best for them," the Argentine midfielder said.
"The pitch? It was bad, but I do not think that Milan wanted to play on a pitch like that either. It is just that they are not able to find a solution to this problem."
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