The Scotland international, who opened the scoring for West Brom, reportedly made a gesture to the Stoke fans in response to heckles from the crowd.
Morrison appeared to place his left hand on his right upper arm and deliver a fist-pump gesture towards home supporters.
When questioned about the incident, Hodgson was quick to defend his player and admitted that he did not see it himself.
"Did he do that? Blimey. You guys (the media) see everything," said Hodgson.
"That gesture could be interpreted in a thousand ways.
"I hope he didn't do a gesture. If he did, I'm sure he'll apologise for it."
Morrison has made 139 appearances for the Baggies since moving from Middlesbrough in 2007.