The prolific attacker was left impressed with the Liga leader's victory and stressed that everything went exactly as Barca planned.
Two goals from the Argentine attacker gifted Barca a two-goal lead at half-time, before David Villa and Jordi Alba poured more salt in Milan's wounds after the interval to erase the 2-0 loss from the first leg at San Siro, and help the Catalans to the quarterfinals of the competition.
"Really, we needed a night just like that not only to get through but to erase that result in Milan. Everything came off perfectly," Messi said, according to the official UEFA website. "We did it. From the fifth minute when we got that important first goal, we just went after Milan in every moment.
"We wanted that opening goal as soon as possible in the match not only to cut the deficit but to make the fans feel it was going to happen. It was a really lightning quick movement of the ball to get it to me and, happily, I put it away."
The prolific attacker then went on to stress that Barcelona were back to their usual best again after a number of difficult games.
"Perhaps in the last few matches we've lost a little of our form. We knew, however, that to go through this tie all we really needed was to get back to being ourselves.
"We envisaged what kind of performance this needed to be and how to produce it. This is the Barca that we and our fans want to see every game. This is the kind of performance we've been producing for years."
The draw for the quarter-finals takes place in Nyon on Friday.