The Dons battled through difficult conditions and after a tough opening half-hour, took control before the break thanks to goals from Ryan Christie and Stevie May.
Greg Stewart scored twice in the second half, with substitute Matty Willock replying for the visitors.
McInnes said: “In fairness to both sets of players, it’s difficult conditions out there and there’s a pattern to me saying that after home games at the moment. It’s a challenge to bring a bit of quality.
“We had to take responsibility to get on the ball and try to pass it around, and Kenny McLean and Graeme Shinnie tried to do that today.
“The first goal was on the counter and with the pace we have in the team we can go from box-to-box rather quickly.
“Once we got the goal, I thought we were very good afterwards and we went in at half-time with a lead I think we deserved.
“For us to produce as much attacking play as we did, albeit it in spells, it was very exciting, and the front four players all contributed.
“Greg Stewart I’m particularly pleased for. By his own admission he’s probably not done enough to go and play week-in, week-out. He’s played his way into the team through his training.
“We had a sense he was ready to go in, and he made a big impact.”
St Johnstone boss Tommy Wright was clearly far from happy with his side and slammed the mistakes that have cost them so often this season.
The opening goal came while Denny Johnstone was receiving treatment for a facial injury, but Wright said: “I could use that as an excuse for losing the goal, but I won’t because we should deal with it.
“Derek’s highlighted that the pitch is poor and we picked the team thinking there wouldn’t be much football played. Up until the goal we probably edged it and although we hadn’t worked the goalkeeper, we were comfortable.
“We had a five-minute spell where we gave away two crazy goals. Aberdeen have played well, but from my point of view all four are poor goals to give away.
“It sums up our season. We’ve been doing well in games, make mistakes, get punished and can’t get back into them.”