Andrew Considine's early goal at Firhill sent them through and the Dons have scored eight goals without reply in three meetings against Thistle this season.
McInnes was satisfied with the manner of the fourth-round win.
"It was important Thistle saw an Aberdeen team that was ready to go again. They have taken a couple of sore ones from us," he said.
"When you score an early goal sometimes it can put a bit of doubt into their heads, and there might have been an element of that because we were dominant in the first half.
"I felt our first-half approach and performance more than merited us going through.
"We are grateful that the opportunities we squandered never came back to bite us.
"But the first half, I thought we did all aspects of the game very well. We were aggressive, energetic, physical, bright in possession. The only thing that was missing was a second goal."
Thistle boss Alan Archibald added: "The start kills us.
"It takes the wind out of your sails and kills your game plan. I thought it affected us in the first half to be honest.
"It's something that has been a problem this season even though we have worked on it. I thought we had sorted it out last week because we defended well.
"I thought the second half was a lot better, we played the game in their half. We could have worked (Jamie) Langfield a bit more and things weren't going for us in the box."