The Swans open the season with a match against the Premier League holders at the Liberty Stadium and the 25-year-old is keen for his side to seize all three points
The match between the two sides at the Liberty Stadium last season finished in a 1-1 draw, before the Swans lost narrowly 2-1 in Sir Alex Ferguson's last game as Red Devils boss at Old Trafford.
And Dyer hopes that his side can improve and put their added match practice to use following their involvement in the Europa League qualifying stages when they take on David Moyes's team.
|SWANSEA v MAN UTD
|11/1||Swansea are 11/1 with Paddy Power to beat Manchester United 2-1
"As a club we've always taken one game at a time – that's the way you need to be to not get caught looking weeks ahead as that is when things start to go wrong. But, to have United first up, it can't get any better.
"To have them so early you definitely want to try and catch them cold. When you play a team like that in the season and they're free-flowing it makes it tougher."
The current Capital One Cup holders have added a number of new faces as Michael Laudrup looks to build on last season's success and Dyer believes that the club deserves praise for their recent achievements.
"You have to give us credit, we're a good side and we've shown we can give any team in the Premier League a game," he added.
"Since I've come here every season has got better and better and the squad has improved again."