Holders Barca knocked the ball about better and had a number of chances but Inter could also have stolen victory with more conviction in the final third.
"It is never easy playing against Italian teams but I'm very proud we tried to win the game. We lacked a bit of precision," Barcelona coach Pep Guardiola told a news conference.
Barca's Ibrahimovic, on his first visit back to the San Siro since his swap deal with Eto'o, rushed a good early opportunity and could only lash wide.
The miss led to a chorus of boos, which had also greeted his name when the teams were read out before kickoff, despite many Inter fans saying they would neither jeer nor cheer their former talisman.
The home crowd could only marvel at some of Lionel Messi's touches, although the Argentine scooped a sitter over the bar following Thierry Henry's cross-shot in the second half.
TOUGH CHALLENGES
Inter's defence were occasionally at sea in the pouring rain and Barca had a penalty appeal for handball turned down, but generally Ibrahimovic was kept quiet.
Eto'o also had to put up with some tough challenges from his former Catalan team mates and, although he was tidy, the Cameroon striker failed to offer any real goalthreat.
Substitute Dejan Stankovic had the best opportunity for the Italian champions when his thunderous drive flew just wide shortly after he had come on.
Wesley Sneijder also went close twice from distance for the hosts but striker Diego Milito was off-colour all game.
"From the bench I saw two teams with great respect for their opponents, two teams well-organised in defence who gave little away," Inter coach Jose Mourinho said.
"In the second half Barca were better than us. Barca are the best team in Europe, not just the champions. An Inter under construction have done very well. If we scored we would have won but without deserving it."
