The centre-back was booked in the dressing room at half-time after a bit of pushing and shoving in the tunnel as the teams walked off at Old Trafford on Saturday.
Reports suggested the bad feeling between the two continued after the final whistle and it has been claimed it was related to Shawcross breaking the leg of Aaron Ramsey - Van Persie's former team-mate at Arsenal - in 2010.
Hughes insisted he knew nothing of the reasons for the incident but did reject the suggestion further intervention was needed to put an end to the apparent long-running animosity against the defender.
"I don't think that was the reason there was an incident but we haven't really discussed that in terms of detail and what was said so I can't enlighten you," said the Potters boss.
"Maybe there were a few petty things going on but they resolve themselves.
"Sometimes it's just better to get on with it. The half had finished and I would have thought the natural break in proceedings would have allowed everyone to calm down, which they did.
"In the second half there was no inclination from anyone on either side to carry on.
"It's just one of those things that flares up very quickly and is extinguished just as quickly."
Hughes takes his side to Sky Bet Championship side Birmingham looking for a Capital One Cup lift which will boost league form which has seen them take two points from the last six matches.
"We are enjoying playing at the moment but we need to get results, we can't keep patting ourselves on the back and say we are playing well we need to start winning," added the Welshman.
"I've always said cup competitions can help your league form so if you get on a good run in the cup it can filter into your league form so it is an important game for us.
"We will be strong because I've always picked strong sides if you a look at the teams I've picked this year and in previous years at different clubs.
"I've always tried to give the competition the respect it deserves and we are edging towards the latter stages so why wouldn't we go strong?
"I'll make changes - some might be forced and others because I want to look at certain things - but we'll go with a team capable of winning the game.
"The competition has been quite good to me (he won it three times with different clubs) and I've always enjoyed cup competitions.
"I'd love to be able to take Stoke to a Wembley final, that was the aim at the start of the season.
"Birmingham are strong at home and caused an upset against Swansea so we won't take them lightly but we feel we can progress.
"Their crowd is passionate and demands that of them so it is not an easy fixture for us by any stretch of the imagination."