The Gers were a goal down after a 14th minute strike from Dylan Lawrence, but goals from Kane Ritchie-Hosler, Aaron Lyall, Chris McKee and Murray Miller saw them come back to win 4-1 in Dingwall.
Thomson was pleased with the reaction from the players, speaking to RangersTV after the game, he said: “Obviously we’re delighted, sometimes when you play in cup competitions it is just about winning, it is the DNA of the club the boys know that.
“We challenged them at half-time I thought we made a sloppy start. I think second-half showed what we are all about, the way we moved the ball around, the players took ownership of that.
“I was actually pleased that we went a goal behind because we deserved to go behind.
“I thought Ross County were well set-up and well organised and fair play to them. I think we expected that we played them obviously only a couple of weeks ago so we did get a wee insight into what they are all about.
With the Gers now in the last eight of the competition, Thomson says they will look forward to next week’s draw.
He continued: “We obviously sit back now, I don’t know what the results of the other teams are but we will look forward to it.
“We have obviously been up here three weeks in a row now so we can enjoy our last bus journey back down the road and we’ll look forward to whoever we get in the next round.”