Victory in Perth took Aberdeen level on points with Celtic at the top of the Scottish Premiership, and extends the team's unbeaten league run to 12 games.
The Dons battled to a 2-1 win over Celtic on Wednesday, and many thought the team's eyes would be off the ball when they headed to McDiarmid Park three days later.
And McInnes believes the thrilling 4-3 win over the Saints proves those naysayers wrong.
He said: "It continues our run. We are over three months unbeaten in the league.
"People keep asking if Aberdeen can handle it. We are doing that. They have done it for ages now.
"There was a big support and a lot was expected of us. Physically this was going to be a tougher game than Wednesday."
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