Two goals late in the second half from Thomas Muller and Miroslav Klose saw last season's double winners defeat the side who came closest to challenging them in Germany last season, but Van Gaal admitted there is still a lot of room for improvement.

"I think that we are a bit further ahead than we were at this time last year and the players have understood what we want and everybody knows what they have to do, but we can still improve as individuals and take another step forwards," he said.

"We still must improve from game to game."

Schalke manager Felix Magath admitted his side have a lot of work to do if they are to bridge the gap between the two clubs and challenge Bayern again this season.

Nevertheless, he was satisfied that his half-time team talk had at least brought a marked improvement to his side.

"I was very disappointed in the first half," he said. "The second half was better and it is a shame that we made an error for them to lead 1-0.

"The game was open in the second half and we could have won it, but considering the first half, Bayern deserved to win."