The Bees lost 1-0 via Phil Foden's first-half City strike.
Jansson said, "I think we started the game very well, created some good chances. Came close to scoring and it would have been a different game. They scored and that was hard after our good start.
"I can't say we were close to a point but we were in the game, I think it's a performance we can be proud of.
"We play against probably the best team in the world and when they have the lead, they keep possession. I don't think they created that many chances, so apart from their goal I think we defended well.
"When it was 1-0, we know there is always a chance - we fought until the end and it's a performance we can take a lot from."
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