Rangers looked to be heading towards victory after turning the contest on its head in the second half, but they were pegged back when Callum Burnside was shown a straight red card and Clyde levelled with four minutes remaining.
However, there was a late twist in the tale when Alex Lowry netted deep into stoppage time, adding his second goal of the evening to seal Rangers’ place in the next round of the competition.
Speaking to RangersTV after the victory, Thomson commented: “I thought it was a thoroughly entertaining game.
“We were definitely in control in the first half, but we went in 1-0 down having lost the penalty.
“As a young player at Rangers, you need to be able to compete against these teams such as Clyde tonight.
“The young boys certainly are handling it, but there also needs to be some credit going to the older players.
“There was a fair bit of discussion between the players when we went in at half-time, which was healthy.
“Everyone knows the demands at Rangers, and you need to show a fire and relentlessness which the fans certainly saw tonight.”
The young Gers trudged in at the interval behind when Logan Dunachie dispatched from the penalty spot.
However, they emerged for the second half with a renewed purpose and soon found themselves ahead through well-taken goals from Lowry and Burnside.
The side then had to show resilience following Burnside’s dismissal to snatch victory when a penalty shootout looked inevitable.
Thomson added: “We wanted to have more purpose when we were creating attacks. I thought the speed of our passing wasn’t what it should have been.
“We turned back more often than not and retained the ball when we really should have went forward and tried to cut Clyde open.
“We had a better shape about ourselves in the second half when we didn’t have the ball; we were more compact and harder to play through.
“You need to have something different from the others if you play for Rangers Football Club. We had a lot of good players in our lineup tonight, both young and on the older side.
“We know that there is pace in the team and that they can handle the football. If I go back to the first half, we didn’t play with much purpose.
“But I thought we showed character, personality and we certainly won the game in the second half.”