Much was made of Louis van Gaal's era in charge of United beginning at Old Trafford in the opening game of the new Premier League season, but Swansea spoiled the party with an excellent victory.
New United captain Wayne Rooney cancelled out Ki Sung-yueng's opener eight minutes into the second half and the England star then hit the post with an excellent free-kick as the hosts ramped up the pressure.
But United, who never looked comfortable in either of the 3-4-1-2 and 4-4-1-1 systems employed by Van Gaal, were stunned when, with 18 minutes remaining, Gylfi Sigurdsson powered home from close range.
Monk – who spent 10 years at Swansea as a player before making the step up to head coach – said his pre-match message was about ignoring the distractions, something his side did admirably.
"I'm happy but not because it was against Manchester United because all I care about is the three points," Monk said.
"That's what I made the players worry about all week. I told them not to care it was Manchester United, the first game of the season, with all the nerves.
"I reminded them it was just another grass pitch and 11 players against 11.
"It's not that Old Trafford has lost a fear factor - this is Manchester United with the history it is steeped in, the resources they have, the players out on the pitch even considering the injuries they had.
"But I didn't care, all I cared about was us. It doesn't matter where you go, you have to make sure the focus is on what you do, no matter who you play because if you're not right, you'll lose the game.
"We were right in many areas and got the right result."
Monk also felt that Swansea's status as rank outsiders was used as motivation for his squad.
"I can pretty much guarantee no-one outside of Swansea gave us a hope," he added.
"So I told the players to go and show exactly what we're about."
The win was Swansea's second at Old Trafford in 2014. The Welsh club won by the same scoreline in the third round of last year's FA Cup.
