McManaman headed for an early bath just three minutes after coming on as a substitute in the 56th minute after a heavy challenge on Brett Pitman, who also had a penalty saved.
Lewis Grabban netted the only goal of the fiercely contested battle on the south coast after 42 minutes, latching on to a calamitous back pass from James Perch.
The game exploded into life after the break but ex-Bolton boss Coyle feels the FA Cup-winning midfielder, who made all the wrong headlines for a horror tackle on Massadio Haidara last season, won the ball fairly.
He said: "We all saw what happened but I was one yard from the incident and Callum clearly won the ball. There is no doubt his momentum took him into the lad.
"We all want decisions but I would not ask my players to run after the referee to get players sent off.
"If someone beats me fair and square I will hold my hand up, but I am not convinced that happened.
"I will certainly be appealing. If someone wins the ball clearly like that. I think he got it wrong.
"I thought the penalty award was soft as well and it seemed every decision that was given went against Wigan Athletic but that is the way it can go sometimes.
"The referee has a duty to do and sometimes he will get it right and sometimes he will get it wrong but he should be left to his own devices.
"Ideally in the Championship you want a level playing field and I am not convinced we got it but we go into the next games ready for the challenge."
Cherries top-scorer from last season Pitman had the chance to put the game to bed shortly after the break when he was awarded a spot-kick after being bundled over by Jean Beausejour.
But former England stopper Scott Carson, who also made a great save from Grabban in the first minute, guessed correctly down to his right to keep his side in the game.
Wigan were up against it and only came close to equalising when Marc Pugh hacked a Leon Barnett header off the line late on.
Bournemouth boss Eddie Howe hailed a great win for his side.
He said: "It is a big scalp. To beat the FA Cup holders at full strength cannot be underestimated. It is a great win even though they were reduced to 10 men.
"There were some naughty tackles in the game in the build-up to the red card. I thought it was a high challenge and his exuberance took him in a bit quick.
"I don't think it was malicious but I think it was a red card. He doesn't have a reputation, referees judge the tackles on their merit.
"These two wins really show what we are capable of and give the players confidence."