The Ghana international was thrilled to score his first Champions League goal to seal the win, while M'Baye Niang praised the 2-0 triumph as "the perfect score"
Muntari struck a superb volley to seal the win after compatriot Kevin-Prince Boateng had given the Rossoneri a well-deserved lead early in the second half, and the former Inter man was thrilled to be on the scoresheet for the first time in Europe's premier tournament.
He told Sky Sports after the match: "I was telling my wife I've never scored in the Champions League, and it came today! I'm really surprised, but really happy, both for the goal and the win for the team.
"We listened to our coach, he did a fantastic job. We were very disciplined on the pitch and we managed to close every angle. Barcelona is the top club in the world, they have amazing players, and if you play without concentration, they will make you suffer.
"Two-nil is a lot, but playing in Camp Nou is not easy. We have this advantage and we will try to do well."
Such was Milan's stoic defensive display, Barca were limited to just two efforts on target in the 90 minutes, and full-back Kevin Constant was pleased that their planning came together on the night.
"During the week, we worked hard on the defensive side," he told BeIn Sport. "We knew Barca would possess the ball, we were prepared. We also knew we would have chances and we took advantage of them.
"It's a step further. It's something good. But we know that it will be very different in Barcelona. It is up to us to recover well and do it again."
M'Baye Niang feels his side could have done more to add to their two-goal tally, but insisted he was perfectly happy to take a healthy lead to Camp Nou in March.
"It is the perfect score," he remarked to BeIn Sport. "Even if we missed some opportunities we won't spit on this result when we are facing the best team in the world.
"It is a good omen for the return game. It is fully deserved. We wanted to play a great game in front of our fans. We had to win and we did so in a very good fashion.
"But with Barca, you never know. We have a good advantage, let's do the same game again."