Van Persie's former team-mate suffered a career-threatening leg-break in 2010 at the hands of the Potters defender, which was thought to have been the reason behind the pair's conflict on Saturday.
Shawcross was booked during half-time due to pushing and shoving among the duo as they headed into the dressing-rooms but Hughes downplayed the incident's severity.
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"Maybe there were a few petty things going on but they resolve themselves. Sometimes it's just better to get on with it.
"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."
The Potters took the lead against United twice but were unable to prevent a comeback win by the Red Devils, who eventually won 3-2 with goals from Van Persie, Wayne Rooney and Chicharito.
The Potters travel to face Birmingham for the fourth round of the Capital One Cup.