The Swans began their campaign in the perfect fashion as they secured a 2-1 victory at Old Trafford over Louis van Gaal's men.
Monk believes that his team have to keep up their intensity in their second match of the season against Burnley.
He told reporters: "They may have lost against Chelsea but they have a team coming here full of confidence, they will be thinking this is where their season starts and we have to match them.
"The biggest reason we won the game last week was that we worked harder than United, in every aspect.
"We can't just say we're in our fourth season in the Premier League and we should win, I haven't allowed the players to do that and that will be the message on the day of the game."
Swansea take on Burnley at the Liberty Stadium later today.