Bayern picked up their fourth straight win on Wednesday to give them an unassailable eight-point lead before their remaining Group E matches at bottom side Manchester City and home to CSKA Moscow next month.
Goals by France winger Franck Ribery and Germany's Mario Goetze sealed the victory which put the Bavarians into the last 16 with a perfect 12 points so far.
But Guardiola expects to be without left-back Alaba for the next few months after the Austria international damaged his medial knee ligament.
A full diagnosis will be known after Thursday's scan.
"It's a real pity, he's really important for us, but it looks like he will be out for two or three months and he'll play again after Christmas," said Guardiola.
"It's always a bit difficult without him, but we are also playing well without the likes of Bastian (Schweinsteiger) and Thiago (Alcantara, who both have ankle injuries)."
As Guardiola had predicted, the hosts encountered a far more robust Roma defence compared to their record 7-1 routing of the Italians in Rome a fortnight ago.
"Of course, I am very, very happy with the result and congratulate all my players," added Guardiola, whose team are four points clear in the German league.
"We had a few problems to find our rhythm, but we played better in the second-half.
"We're in the last 16, which means we can focus on the Bundesliga now."
Despite losing to Bayern home and away, Roma are still primed to join Munich in the knock-out phase as they stay second in the group, but level on four points with CSKA whom they play away in three weeks.
"We can leave here with our heads held high and that was our goal here," said Roma coach Rudi Garcia.
"I think we cancelled the bad image of the game in Rome.
"We were brave, ran a lot and the front two did well.
"It's hard for the strikers to create much up front when they have only 30 percent possession.
"We are aware that Bayern are a couple of steps ahead of us right now so we tried to adapt.
"They are a very strong side and they proved it once again."
Roma midfielder Radja Nainggolan said the Italians still had everything to play for with the last 16 within reach.
"It was important not to concede many goals after the bad defeat in Rome," said the Belgium international.
"After facing Bayern twice, we are still second in the group so we have a good chance to qualify and we will do everything we can in the last two games."