Goals from Gylfi Sigurdsson and Ki Sung-Yueng handed the Swans a 2-1 win at Old Trafford on Saturday in the opening game of the new season.
The victory marked the second time in 2014 that the Welsh club have triumphed at United following an FA Cup third-round success back in January but Monk is keen for his team to avoid complacency and believes that they are capable of producing more polished performances.
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"We can be sharper in certain areas, but the whole key to it all was us coming together as a group, working for each other, and I think everyone saw that.
"We've worked very hard in pre-season, putting structures in place where we could adapt to different situations and it was very pleasing we did that for most of the game and limit Manchester United to very little chances."
Wayne Rooney's close-range overhead kick cancelled out Ki's opener before Sigurdsson stunned the home fans 18 minutes from time.
Swansea boss Monk added: "The disappointing thing was conceding from a set-piece and the marking involved but the character to come back shows what we've got in the squad. Now we have to make sure we prepare as best as possible every week and to perform as consistently as we can.
"There will be days when we lose but hopefully there will be more days like this."