The Welsh club have made a great start to the Premier League season, picking up a shock 2-1 win at Manchester United before earning a hard-fought 1-0 victory over Burnley on Saturday.
With the season still in its infancy, those results put Swansea among the English top flight's early leading pack, but Monk insists he will not allow his squad to get carried away ahead of Tuesday's second round match.
"It's great to have six points, of course it is," he said. "But we've got a game Tuesday and that's all I focus on.
"It's the best start we could have had in terms of the two games, but you know you're only ever one or two games away from people being on your back or not performing well or getting dragged back into certain areas of the league.
"We'll just keep doing what we're doing, try and build on the mistakes that we make and make sure we improve on them, but ultimately we try and win as many games as possible."
Swansea, of course, have happy memories of this competition in recent years.
Under then-manager Michael Laudrup, the Liberty Stadium outfit lifted the trophy in 2012, but their defence fell at the first hurdle as they were defeated by Birmingham City in the third round last season.
Rotherham were eliminated at this stage by Premier League side Aston Villa a year ago, and defeated Fleetwood Town in extra time to set up their tie against Swansea.
Monk has named the same starting XI in both of Swansea's Premier League matches so far, but could well use Tuesday's match to rotate his squad with West Brom set to visit the Liberty on Saturday.
New signings Bafetimbi Gomis and Jefferson Montero have had to make do with a place on the Swansea bench until now, but Monk may view this as an ideal chance to utilise them from the start.
There could also be a place for latest arrivals Federico Fernandez and Tom Carroll, while youngsters such as Josh Sheehan - an unused substitute in both league fixtures - may have an opportunity to get some minutes under their belt.
Rotherham's start to life in the Championship has got off to a steady start, with two wins and two defeats to show from their opening four fixtures.
Former Swansea loanee Febian Brandy is yet to make his Rotherham debut after joining the club on a free transfer, so will be hoping to make his bow on familiar territory.
Leon Britton and Marvin Emnes are unlikely to feature for the hosts as they continue to recover from knee injuries.
