The Catalan giants were in the driving seat for most of the match, but could not convert their superiority into goals as Guardiola's men failed to find the target for only the fourth time in 2011-12.
"We played well, we had possession of the ball and we dominated," Guardiola told reporters after their quarter-final first-leg encounter.
"At half-time, I told my players not to take too many risks, but despite that we had 17 shots on target while playing with nine players from our youth ranks.
"We played like ourselves in a match which was really demanding. Milan are satisfied with the result and that is the biggest compliment we can get from a club with seven European Cups.
"The fans must show up in the second leg. These players have given too many things to be left alone. I know that the fans will come."
Guardiola then followed in the footsteps of Arsenal manager Arsene Wenger, who was highly critical of the condition of the pitch at San Siro during the Gunners' Round of 16 tie against the Rossoneri.
"Milan should take some measures," Guardiola explained. "We play where we are told to play, but I do not think that Inter and Milan want a pitch with these conditions.
"It is bad for the spectacle, but to be champions we must overcome all adversities. We have done this many times, although people say otherwise."
Barca duo Carles Puyol and Victor Valdes were very critical of the refereeing decisions in the match, but Guardiola refused to comment on the officials' work.
"If the referee did not award us those two penalties, it is because he did not see them," the 41-year-old said.
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