The first leg of their UEFA Champions League quarter-final ended level following second-half goals from Nemanja Vidic and Bastian Schweinsteiger.
While the latter was sent off late on after picking up a second yellow card, Bayern remain favourites to progress having secured an away goal ahead of next week's second leg in Munich.
Coach Guardiola, who is looking to emulate predecessor Jupp Heynckes by securing a treble, acknowledged the challenge his side faced in attempting to break down a disciplined United outfit.
"It's not easy against a team that put so many bodies behind the ball. We scored an away goal. That's important," he said.
"We will try to win the return leg. I have complete faith in my players.
"We scored an away goal, which is important, but we also got lucky that efforts from (Danny) Welbeck and (Wayne) Rooney did not go in. The goal we conceded was difficult to defend.
"It is always dangerous when you go into the second leg with a 1-1 draw, but even a 2-1 victory would have been dangerous.
"I am sure we can do it. I have full confidence in my players and hope the fans in Munich will push us like the United supporters did for their team."
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