The Swans impressed throughout the first half at the Emirates Stadium and, although the Gunners improved in the second period, they were unable to break through before the attacking midfielder's match-winning strikes.
"Michu is so good in those situations as we've seen already this season," Britton told The Sun.
"He had so long for the second goal but he showed great composure."
The midfielder was on the Gunners' books for seven years as a youngster before moving to West Ham for £400,000, then a British record for a 16-year-old, and says that, while it was nice to get a deserved win, they cannot afford to dwell on it for too long.
|SWANS v CANARIES|
|14/1||Swansea City are 14/1 with Bet365 to beat Norwich City 3-1|
"It's just fantastic to get the win because they're a great side. Arsenal had a lot of possession but - on chances - we edged it. We deserved to win.
"We can't get carried away. We'll enjoy it for 48 hours before looking ahead to Norwich."
Michael Laudrup's side are now level with sixth-placed Everton on 23 points after a six-match unbeaten run but host Norwich City on Saturday, with their opponents having gone eight games without defeat.