The experienced official awarded Cherries a second-half spot kick for handball against Shakers defender Matt Doherty and then reversed his decision after consulting his assistant.
Boyeson, who appeared well placed to view the incident, took several seconds to point to the spot, only to signal for a corner after speaking with the linesman who was on the opposite side of the pitch.
And while opinion was divided as to whether or not Boyeson had made the correct decision, Howe fears the Hull-based official could face ramifications when taking charge of future matches.
Howe, who spoke to Boyeson as the teams left the pitch at the final whistle, told the Daily Echo: “He said he thought it was a penalty and, as soon as he had made the decision, he thought it was a bad one.
“I know there was an arm raised and, whether it hit his arm or not, it didn’t take away from the fact that the referee gave a penalty and then decided to change his mind. Whether it was or wasn’t, he shouldn’t have given it in the first place if he wasn’t certain.
“That type of scenario is just going to encourage players to protest and you will have players in the faces of referees and linesmen. I wouldn’t want to see a penalty given if it wasn’t but, once you give the decision, you have got to stick with it.
“It was just the fact that he changed his mind because that was a dangerous thing to do. If you are an official and players get wind of it, you will just have melee upon melee after decisions you feel are contentious.”
The incident, which came after Doherty had climbed at the far post to defend a Simon Francis cross, took place when Bury were leading 1-0 thanks to Troy Hewitt’s stunning 14th-minute opener.
However, after Lewis Grabban had struck to restore parity and David Worrall had netted to restore the Shakers’ advantage, Brett Pitman came off the bench to grab a dramatic injury-time equaliser.
Speaking about the penalty decision, Bury manager Kevin Blackwell said: “I have got to give praise to the referee. You see referees who are so arrogant that they feel that if they change their mind, it is a flaw or a weakness.
“He took his time, he spoke to his linesman and they both said he had headed it out. There was an arm up but it was for balance. He made the correct decision.”
Cherries midfielder Harry Arter picked up his fifth booking of the season and an automatic one-match suspension for protesting the decision. He will sit out the FA Cup second round clash at Carlisle.