Wolfsburg fell behind early on to a goal from Thomas Muller, but they levelled in the second half through Edin Dzeko and had chances to win the game before Schweinsteiger grabbed the winner in stoppage time.

"That is the worst possible way to lose a game," said McClaren, who became the first Englishman to take charge a Bundesliga side last night.

"It is obviously hugely disappointing for us.

"We came back into the game with lots of passion in the second half after showing too much respect in the first half.

"It has taught us a lesson, but something like that hurts."

Many will say that it was a typical way for Bayern to win a match with a goal in the last minute, but their coach Louis van Gaal insisted that his team had deserved the victory for the way they improved towards the end of the second half.

"I think we came out of the dressing room (for the second half) a bit overzealously, but then we played with a lot of impetus and in the end that is how we got another goal," he said.

"It is a victory and three points and that makes me happy because it was very tough."

Bayern needed four matches before winning for the first time last season so their chairman Karl-Heinz Rummenigge was particularly happy not to have to wait so long this time around.

"Overall, it was important to start with a win," he told his club's website. "That gives us some peace and self-confidence at the same time."

Bayern's next game is a trip to Kaiserslautern next Friday night while McClaren makes his home debut in Wolfsburg against Mainz next Saturday.