Messi hit his 52nd and 53rd goals of the season inside the opening 40 minutes at the Nou Camp as Barca wasted no time in wiping out Milan's 2-0 lead from the first leg in Italy.
David Villa put Roura's men in front in the tie for the first time with a third goal after the break, but Barca remained only a goal away from elimination and needed Jordi Alba's late strike to finally set the seal on the victory.
Assistant coach Roura, again in charge of Barcelona with Tito Vilanova undergoing cancer treatment, revelled in a "special" occasion for the Nou Camp faithful, but was in no doubt about who deserved the lion's share of the credit.
"Leo gave us a majestic lesson in what it means to play football," Roura said.
"He's an extraordinary player and when he's surrounded by the best he has no limits."
Reflecting on the recent run that saw Barca lose twice to Real Madrid in the wake of the first-leg defeat in Milan, Roura added: "The players were overly criticised and they showed that they are special.
"They played with intensity, commitment and that should make us proud. I'm very pleased.
"We had a very clear idea of how we needed to play. At the break we were right where we wanted to be, level on aggregate. I told the players to be calm.
"Frankly it was pretty difficult when we were up 3-0 and it seemed as though Milan could have scored from any play.
"We controlled the tempo of the match and with the 4-0 it was over.
"We're going through to the next round because we kept a clean sheet."
Roura had further good news for Barcelona's fans after the match when he indicated that Vilanova could return in time for next month's quarter-final tie.
Remember for years
However, he stopped short of saying whether that would be in the dugout or merely as an observer in the stands.
"Tito Vilanova is very happy and he'll be here for the next round of play," he said.
Barcelona's director of football Andoni Zubizarreta also heaped praise on Barca's players as they became the first team to overturn a 2-0 first-leg deficit in the Champions League.
"We will remember this for years," said the former Barcelona and Spain goalkeeper.
"From the very first minute we pressured them really well high up the pitch and we didn't let them think.
"They've shown us why they are in the Champions League, but I believe we played an excellent match."
Midfielder Andres Iniesta added: "We achieved our objective. To date it was one of the most complete games we've played. Hopefully this experience will help us in the future.
"We had an obligation to try and fight back and that's what we did.
"The feelings we transmitted on the pitch were fantastic. When we show our identity, we're very hard to beat."
Full-back Dani Alves was equally enthused by the performance, saying: "I think that, once again, the members and the fans left the stadium with a sense of pride.
"We aren't the team that lost to Milan. We're the team that won this evening.
"We pressured, created chances. This is the team's identity.
"On this magical night we defeated a great rival."