Danny Rose equalised from the resulting free-kick which flew over everyone and deceived goalkeeper Matt Ingram.
Morgan put Wycombe in the lead once more from the penalty spot and they looked like they were heading for a surprise win until James Constable knocked the ball back to Mullins who drilled home a dramatic leveller.
"That was a great point for us," Ainsworth said. "And it's a great turnaround after Mansfield. You worry after performances like last week but my players were terrific with 10 men for half an hour.
"I'm immensely proud of them, they gave me everything they had.
"I thought there was a foul leading up to the goal at the end and the decision not to give a foul then was very disappointing. My lads are down, but they should be proud.
"It showed me last week against Mansfield was just a blip.
"And Dean Morgan coming back in and scoring two goals, and playing the way he did, shows me he wants to be in the team."
Ainsworth did not want to make a judgement on whether Dunne deserved his red card for what the referee deemed was an elbow in the face of Potter.
"We'll have to look at the DVD of it," he said. "If he did catch him in the face with an elbow, it was an accident in Charles's view.
"The biggest disappointment for me is to lose him now for three games."