The Argentine acknowledged that Massimiliano Allegri's men put up a good fight, but feels that his team made perfect use of their strengths to eliminate the Rossoneri
The Catalans were held to a scoreless draw in the first leg, but two goals from Messi and an Andres Iniesta strike helped Barca to a comfortable home win in the return to book their ticket for the semi-finals for a fifth straight year.
The Argentine admitted that the Rossoneri made life difficult for the Blaugrana, but praised his team for digging deep to get the result.
"We knew, quite clearly, that this was going to be a tough game. What was vital is that we also knew how to take advantage of our strengths and because of that we won and we are through," Messi said to uefa.com.
"Milan have great footballers and they are demonstrating their quality in the Italian championship and this Champions League again.
"Like the first leg this was a hard contest but we did well and we are through."
Barcelona will meet either Chelsea or Benfica in the semi-finals of the Champions League. The Premier League side defend a 1-0 lead from the first leg in Wednesday's return at Stamford Bridge.