"It's been a difficult few days for everyone. We are all used to managers leaving because sadly that has always been part of the game," Curtis told the club's website (www.swanseacity.net).
"But Garry's departure seemed a lot more personal to everyone because he has been at the club so long.
"We all feel -- staff and players -- that we have let him down and we want to go a small way to rectifying that on Saturday.
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"Yes, we are on a bad run, but we won't be going to the Etihad (Stadium) just to make up the numbers and get the fixture out of the way while we wait for a new manager to come in.
"We need every point we can and we will strive to be competitive and get something out of a difficult game."
Monk took over from Michael Laudrup in February 2014 and in his first full season in charge steered Swansea to eighth place, their highest-ever finish in England's top-flight.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
