Despite a hard-fought win Guardiola has admitted that there is plenty of room for improvement, citing a slack period after the interval that gave Gladbach hope of spoiling Bayern's start to the campaign.
He told reporters in a post-match press conference: "We knew it would be a tough match. It's always hard work against Monchengladbach.
"We had no control over the match in the first 15 minutes of the second half.
"We're satisfied with this first victory, but we need a couple more wins to build up our confidence."
The Bavarians profited from a bizarre double penalty award for their third goal against Gladbach, with Alaba scoring from the spot just one minute after Thomas Muller had his effort saved.