Sunday's win was Swansea's third in a row against United and extended an excellent start to the season which began with an opening-day draw at champions Chelsea.
"We're a good team," Monk told Sky Sports. "We're a force in this league and when we're on it and playing our best football we can be unbelievable.
"When we weren't playing our best we can do the other side and that's the key to being a good team."
The Welsh club were promoted to the Premier League in 2011 and consolidated their top-flight status under first Brendan Rodgers then Michael Laudrup.
They won the 2013 League Cup, their first major silverware, but Laudrup was dismissed and replaced by inexperienced Monk in 2014 -- his first managerial role.
Monk, however, defied the odds by finishing eighth last season with a club record 56 points and Swansea have started this campaign in eye-catching form.
"It's just the way that we work and the stuff I try put in place with he players on the field and off the field we work a lot on our mentality and the way we approach games," said Monk, who has continued the club's recent tradition of possession-based, neat-passing football.
"Today you saw character and the technical side of it. You've seen in the games already this season we've performed unbelievably well and in different ways and shown every side of us. That's what a good club should be doing."
Fundamental to the victory over United was their ability to adapt.
Monk started the game playing 4-2-3-1 with limited success but reverted to a diamond formation and turned the game round with two quick goals through Andre Ayew and Bafetimbi Gomis.
"We thought they were overloading us a bit in the middle so we went to the diamond for 10 minutes in that second half," Monk added.
"I think that helped us get two quickfire goals and at the end we just made a couple of little changes and saw the game out really well."
Monk's counterpart Louis van Gaal said his side's inability to adapt to Swansea's formation change lost them the game.
"They had a shape which they started with and that was 4-2-3-1 and after 1-0 they changed the shape. We couldn't cope with that and that's not good," the Dutchman said.
(Editing by Mitch Phillips)
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