The Doncaster Rovers boss, who was frustrated at the award of a stoppage time penalty against his side, was shown a red card by referee Trevor Kettle for dissent.
Wellens is expected to now have to serve a three-game touchline ban, starting with tomorrow’s visit to Ipswich Town.
Conor Grant converted Plymouth’s second penalty of the game to seal a 2-1 come-from-behind win for his side and inflict a sixth league defeat from eight games on Rovers.
"I apologise to the Plymouth fan,” said Wellens. “I’m not actually sure it hit anybody.
“We gave away a penalty and there’s a water bottle that is empty at the side of my foot and I kick it.
“I don’t know where it went. I’m informed that the fan actually threw it back at me so fair play to him.
“I’ll send an email to Plymouth Football Club and apologise because that’s not acceptable.
“I’ll pay the consequences with a three-game ban and I’ll pay the consequences with whatever the fine is.
“But I spoke to Mike Jones, the head of referees, this morning and he apologises because he thinks that both penalties were harsh and in his opinion they weren’t penalties.
“That’s 11 [major decisions] they’ve got wrong now and we’ve played eight games. They’re things that we can’t control but they obviously frustrate you. You just want a referee to be out of sight and out of mind during a game.
"We’ve just got to control what we can control. I thought we did that very well against Plymouth and I think we should be coming away with definitely a point but we could have easily won the game if it wasn’t for a game-defining moment.”