The Spiders put in a valiant showing at Ibrox but eventually went down 4-0 as two goals from Andy Little and strikes from Ian Black and Dean Shiels extended the Gers' lead at the top of the Irn-Bru First Division.
Queen's had their chances during a tight first-half but fell away after the break as Ally McCoist's side hit top gear.
Speirs handed a starting bow to youngster Blair Spittal and is confident there are positives to be taken from the derby clash despite seeing their impressive recent run of form come to an abrupt end.
"I wouldn't really describe us as surviving in the first half," he said.
"I know Rangers had one or two opportunities but we had some decent passages of play and you hope you might do better.
"When that happens at places like this you have to score and we didn't do that.
"We thought we had given ourselves a reasonable platform for the second half but we have lost two or three disappointing goals and you are always up against it when that happens.
"There was some decent build-up and good inter-play between our players to create chances and opportunities that didn't quite lead to goals.
"That is the positives. A lot of that play was with young players.
"We had a young player who made his starting debut and we were delighted with him.
"He tired obviously but we were delighted with him.
"We took a sore one losing 4-0 but we will stay positive, we will take it on the chin and move on.
"One of the good things about coming to a place like this with the atmosphere and the crowd is that it brings our young players on leaps and bounds.
"The young players confirmed what we thought of them, that they have the necessary temperament and ability to come to these places and play."