The Dons earned a point when Adam Rooney latched on to a short pass-back from Chris Millar to cancel out St Johnstone's opener when Stevie May capitalised on a mistake from Clark Robertson.
McInnes said "We showed plenty of endeavour, but it's not the result we would have wanted. I don't think we brought enough quality to the game.
"The goals from both teams came from defensive errors and I don't think we carved St Johnstone open enough.
"I can't fault the effort and commitment of the players, but we needed to bring more pace and tempo. We weren't at our best, but picked up a point which could prove important come the end of the season."
St Johnstone boss Tommy Wright praised his team's display as they earned their first point of the season against Aberdeen.
Despite relying on a late save from goalkeeper Allan Mannus, the Saints manager reckoned his charges more than deserved the point.
"I've very pleased. It's a good point and a fair result," Wright said. "It's strange that for two teams of such quality we've both scored similar goals that have come from mistakes, but we could have snatched all three points at the end.
"Alan Mannus had to make a good save at the end, so I'm sure Derek McInnes will say Aberdeen could have won it too and I think the share of the points was fair.
"If you look at Aberdeen's record they're particularly strong at home, so I'm pleased with the point and both that and the performance were important.
"We've now taken four points out of six after the split which is very good, and I have to commend the players for our run of form from the end of March onwards."