Scott Vernon and Barry Robson were the goal-scoring heroes, after 20 and 66 minutes respectively, and McInnes said: "Of all the wins we've had this season, that's the most satisfying three points.
"We knew what from early in the week what the conditions would be like, and that the winds were set to be at their strongest at three o'clock on Saturday.
"We knew we would have to try to be brave, keep the ball on the deck, as any high balls would become a lottery.
"And I think both goals were an example of that. Both came from misjudging the ball in the air.
"I think we dealt with the conditions better over the 90 minutes. I still felt we were a bit wasteful with our chances but the supporters should be pleased and proud of the performance."
His opposite number at Saints, Danny Lennon, added: "The conditions played a big part. Today's game was being built up as two good teams coming against each other in good form.
"And they would have come along expecting to see that type of quality but the elements didn't allow that.
"We've got to dust ourselves down and take it on the chin. We've been on a good run lately and we're going to have to get back on that road very quickly.
"The goal we had disallowed was a big call by the official and, from our angle, looked very much onside."