Ryan Jack scored the only goal of the game for the Dons and Saints had chances to get back on terms.
McInnes said: "I anticipated it being a hard game. The onus was on ourselves to start well and get ourselves in front. I felt we moved the ball around quickly and with Ryan Jack getting the early goal it certainly helped.
"We've played St Johnstone three times prior to this and they've created very little if at all against us, we've really kept their chances to a minimum.
"But here they created a lot, got themselves into good positions and I'm sure they'll be kicking themselves that they haven't made more of that because they certainly had two or three of the better chances."
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