Clear-cut chances were limited for both sides throughout the 90 minutes as they shared the points in the Scottish Women’s Premier League.
Speaking to RangersTV at full-time, Thomson said: “I think it was a tight tight game, void of a lot of chances but I think the girls again gave a good account of themselves in terms of their attitude and application and trying to play decent football.
“We never really had a cutting edge in the final third. I think that was evident to see but it is a point and we are still undefeated.
“There were a number of factors, there's a lot of tension and a lot of nervousness about this game which I think the girls have handled and they definitely relaxed into the game. I thought we dominated the first half and in the second-half City came at us and we kind of knew they would do that.
“I think over the piece we have controlled the game without really hurting City and it is something we will need to look at going forward is how we can put a cutting edge on performances.”
Rangers attention now turns to Aberdeen at Broadwood on Wednesday evening and Thomson says the side will have to be ready mentally and physically for the match.
He added: “It is a quick turnaround, the job and the task at hand is something we are all quite aware of so we will have a recovery session on Monday, a session on Tuesday and then we will go into Wednesday's game against Aberdeen.
“Our focus is always there, I think that is a given for us now, I think what we need to do is get ourselves prepared physically and mentally to go into Wednesday's game.”