Bayern won 3-1, with Harry Kane scoring twice - once from the penalty spot - and an own coming via Trevoh Chalobah. Cole Palmer struck for the visitors.
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Kompany said afterwards: "Credit to the lads. In general, it was a very focused performance. In moments I thought we showed a lot of joy in playing the ball and creating chances.
"But we couldn't afford to have a single down period, because the threat and quality of Chelsea was always there.
"We just have to continue and look to win more. I'm not looking too far ahead. We've played one game out of eight. It was a good job, but now we turn the page."