Niall McGinn opened the scoring for Aberdeen, who thrashed Saints 4-0 at the same stage of this season's Scottish League Cup final.
But they missed out on a cup double after Stevie May struck twice for the Perth side in the second half.
"We never had full control of the game," former St Johnstone boss McInnes told Sky Sports.
"Give credit to St Johnstone, they showed real determination to make it their day and we were a bit wasteful. We had three really good chances to get the second goal.
"We spoke about how clinical we were in the last semi-final and that was lacking today, so no real complaints."
McGinn said: "We took our chances in the League Cup semi-final against St Johnstone and they took their chances this time, so we have to wish them all the best.
"Any team would be disappointed to lose a semi-final. There was a big chance for us to go on and do the double, but we have to get back to league action.
"The confidence will be all right. We have good characters in the team and the manager will make sure we will be working hard again."