Bowyer was substituted by Blues manager Alex McLeish midway through the second half of Albion's 3-1 win to avoid the risk of him being sent off.
The former England player had just been yellow-carded following an ugly challenge on Baggies defender Gabriel Tamas.
Bowyer exchanged words with fans situated immediately behind the visitors' dug-out before moving to another seat.
An Albion supporter lodged a complaint with a steward over Bowyer's comments but the matter has been laid to rest after he said sorry.
A West Brom spokesman confirmed: "A fan made a complaint to a steward over comments made by Lee Bowyer after he had been substituted.
"But then Lee Bowyer made an unreserved apology to the supporter and that was the end of the matter."
Bowyer had been unhappy at being on the receiving end of a mis-timed tackle from West Brom full-back Gonzalo Jara which left him needing treatment.
He then took out his frustration on Tamas which led to referee Chris Foy producing the yellow card and caused McLeish to substitute him rather than Alexander Hleb.
McLeish said: "I just didn't want to take a chance. Lee is at a stage of his career where he is much more mature.
"He may have seen the game out but I didn't want to take the chance and get egg on my face.
"Then I think someone blasted Lee when he came off and I saw Lee trying to pacify them.
"I know there were some people having a go from the seats behind the dug-out."
McLeish is demanding a positive response from his side after a series of uncharacteristic errors allowed the Baggies to recover from a half-time deficit.
He said: "Two mistakes set us back a mile. The second half was a major disappointment.
"A lot of the players didn't do enough in the second half to get us back into it.
"It was unlike us but the one thing we are good at is bouncing back.
"We've had one or two performances like that. They are only human and I can't expect them to come back every time."