The Dons scored all four of the goals in the first half with Peter Pawlett and Niall McGinn adding to Barry Robson's brace.
But the visitors had to hold on after the break as Billy McKay's quick double and a late strike from Graeme Shinnie ensured five nervy minutes of stoppage time.
McInnes said: "I was delighted to get the three points. We came here with that objective.
"We managed to get ourselves 4-0 up at half-time, but we knew how dangerous Inverness would be if they got a goal early in the second half.
"I thought in the first half we were excellent. We showed that bit of quality and style, but the big thing for me was the energy of the players and putting the opposition under pressure.
"However, in the second half we opened the door for them and they nearly came right through."
Caley Thistle manager John Hughes praised his team for a spirited display after the break, but was disappointed at their poor start.
Hughes said: "We gave ourselves too much to do, which is unlike us as we've got a great record recently of clean sheets.
"However, we made a better fist of it in the second half. Indeed, I felt like we might have deserved something out of the game.
"We scored three goals, while their goalkeeper has saved from Nick Ross and we've also hit the woodwork.
"I felt Aberdeen scored against the run of play in the first half, but after the penalty Aberdeen were the better team and I'm a little bit disappointed by the manner in which we conceded the next three goals
"At half-time we told the boys to go out and win the second half while giving the fans something to shout about, which we did."
Hughes also admitted that he fears he will be without Richie Foran over the Christmas period through injury.
"It looks like Richie has popped his shoulder," he said. "I'm really disappointed about that, but hopefully, fingers crossed, it will only be a couple of weeks. He'll be a big miss for us."