Shawcross was booked at half time of Stoke's eventual 3-2 defeat to the reigning Premier League champions after confronting Van Persie while he was leaving the field, continuing the incident into the tunnel.
Some claimed that the situation was related to Shawcross breaking the leg of Van Persie's former teammate Aaron Ramsey in 2010, but Hughes was not worried about what caused the issue and believes that it resolved itself.
"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," Hughes told reporters.
"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."
Stoke currently sit 17th in the Premier League table, level on points with 18th-placed Norwich.