Visiting goalkeeper Steve Banks was in excellent form to ensure Saints claimed a point - but McInnes believes his Dons should have been more clinical in front of goal.
He said: "I'm disappointed because I think we had enough chances second half to win the game.
"The first half was much of a muchness. We were tepid to say the least in the first half and, us being the home team, the emphasis is on us to make the difference and try to force the issue.
"We didn't pass the ball and control the game well enough in the first half. We had to make sure that we had more control, and I felt we had that in the second half. It was much more the kind of performance I would expect.
"St Johnstone have their keeper to thank for a number of outstanding saves, and credit to Steve Banks for that."
St Johnstone manager Tommy Wright said: "Parts of the second half we were under pressure, but you have to expect that being away from home to a side of the quality of Aberdeen.
"Most of the chances were from set-plays and shots from outside the box. There was maybe only McGinn's chance where we were opened up. I'm really pleased with how we defended as a team.
"Coming from conceding four goals last week, I've got to be pleased with our performance. We hoped we wouldn't concede and that would give us a platform to go and win the game.
"We did have a few chances in a pretty even first half, but with Aberdeen being the home side we expected them to come at us, and I'm really pleased with how we stood up to that."