"St Mirren were excellent. They were more aggressive and won more battles than us.
"They tired, which is understandable. We got a lift from our first goal and we always looked a threat after that."
St Mirren were 2-0 ahead thanks to strikes from Graham Carey and Andy Dorman before Michael Duberry headed in a scrambled goal for the Perth side on 79 minutes.
And the points were shared when Paul Sheerin tucked away a penalty deep into injury time.
The award was given for a deliberate handball as a St Mirren player kept out a shot from Murray Davidson on the goal-line.
There was no doubt about the award but referee Charlie Richmond delayed proceedings to consult his assistant in an ultimately futile bid to identify the offender.
"There's no question about it, it was a penalty kick," said McInnes.
"I think the referee should have indicated he was giving the penalty right away.
"I can understand if he is not sure who it was - there were a lot of bodies in there. And if he's not sure he can't send anyone off."
We normally start on the front foot and win our individual battles but we didn't ask enough questions today
Derek McInnes
St Mirren manager Gus MacPherson was furious that his side had been denied a penalty for a trip on Billy Mehmet by Saints keeper Graeme Smith, a few minutes after scoring their second goal.
And McInnes admitted his side had been lucky not to be punished.
"It looked a penalty and I can understand Gus's frustration at that one," he explained. "I thought Billy Mehmet should have scored, mind you."
Addressing St Johnstone's sluggish first hour or so, McInnes added: "We normally start on the front foot and win our individual battles but we didn't ask enough questions today.
"At 2-0 down with 20 minutes to go, they looked a beaten team but credit to the players.
"I didn't enjoy today. I normally enjoy watching us - even when we're not playing great, we're always spirited and enthusiastic.
"It looked for long spells that it was a game too many for us."
Source: BBC Sport
Source: BBC Sport