The Potters, who will rest club-record signing Xherdan Shaqiri for the second-round tie, lost their opening Premier League game to Liverpool 1-0 at the Britannia Stadium and have since drawn at Tottenham and Norwich.
Bowen believes performances have been good so far this campaign as Stoke prepare for a third away match on the spin looking to break their duck.
"It is not a concern," Bowen told reporters at the club's press conference on Monday
"Obviously we'd have liked to have won a game but if you look at our performances they have been pleasing
"Liverpool is a difficult game, as they all are, and then two away games
We were certainly saying before a ball was kicked this season that if you can come away from the away games with a point then it is a good point
"And looking back, I think anyone who saw the game against Liverpool would have felt we were the better side
We were unlucky not to get anything out of it
"It is still early days in the season
We would have loved to have a win under our belts but we are not concerned."
Shaqiri will be one of a handful of changes made by manager Mark Hughes but Bowen insists Stoke will still field a strong team against their League Two opponents.
"It gives the manager a chance to give some minutes to squad members," he said.
"We have a strong squad, there is not a lot to choose between those who are starting games and those who are not.
"We are delighted to have this game to get some good game time into those lads who have not been fortunate enough to be involved so far."
Source : PA
Source: PA