The Champions League favourites were condemned to a shock defeat at the San Siro with former Portsmouth stars Muntari and Kevin Prince Boateng claiming the goals.
And Muntari was quick to pay tribute to coach Massimiliano Allegri following the victory.
"We played as a team, we listened to our coach and he did a fantastic job by putting us very well on the pitch," he told Sky Sports.
"We were very disciplined and we closed every angle Barca had so they could not penetrate.
"We were very disciplined, Barcelona is a top club in the world - they play fantastic football and have amazing players and if you play without concentration they will harm you and make you suffer but we knew what we were going to face and it went well so we are happy."
Muntari was celebrating his first goal in the Champions League when he volleyed home nine minutes from time.
"I was telling my wife that I had never scored before so it came today and it was a surprise, I'm really, really happy for the goal and for the team," he continued.
The second leg in Barcelona comes in three weeks and Muntari insists they cannot take anything for granted.
"It is a lot, but in the Camp Nou it is not easy - you could win four or five but they can do crazy things as this is Barcelona - we have two goals advantage and we will try our best to do well."
Goalkeeper Christian Abbiati added on Sky Italia: "We made a big performance, we showed a big sacrifice and spirit.
"We won a big match against a big team. We knew the ball possession would be with Barcelona, but with the coach we prepared a good match, and thanks to our forwards, who also helped on defence, we gave a good performance. Congratulations to the team."