Monk's side handed Louis van Gaal a defeat on his first game in charge at Old Trafford courtesy of goals from Ki Sung-yueng and Gylfi Sigurdsson.
Swansea now take on Premier League newcomers Burnley at the Liberty Stadium after Sean Dyche's men showed signs of promise in their 3-1 defeat to title challengers Chelsea.
Monk acknowledged there was always a danger of losing focus after such an impressive win, but urged his charges to be ready for Burnley's threat.
"There is a concern, which is why I've stressed [this] to them," he said on Thursday.
"We know how important it is to follow up. There are no guarantees but if we can get preparations as best as possible it gives you a chance of delivering a performance you're happy with and you can win a game.
"The most important thing was the three points and it will be the same again this weekend.
"It's always a good feeling to beat big teams and when no-one gives you a chance it makes it sweeter.
"But it's the first game of the season, there's a lot more games to come and I said afterwards we knew can improve on that."
Monk has been busy during the close-season, ahead of what is his first full campaign in charge, bringing in the likes of Federico Fernandez, Bafetimbi Gomis and Jefferson Montero.
Montpellier midfielder Benjamin Stambouli is the latest to be linked with the club and, while Monk stopped short of commenting on specific targets, he remains hopeful of further additions.
"There are targets we're trying to negotiate with, it takes time with clubs and agents involved but hopefully we'll have one or two in before the end of the window," he added.
"Names come up all the time, but until the players are done and dusted I don't want to talk about them.
"Every club tries to identify players but it's not about putting out in public. There are no offers mad, there are offers here there and everywhere."
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