A Jamie Longworth brace saw the Spiders extend their unbeaten start to 2013 and maintain their best of the rest status behind the runaway Ibrox leaders in the Irn-Bru Third Division.
QP's stunning form has them well on course for a play-off place but they had to fight back at Hampden after Martin McNiff and Ally Love netted for Jim Chapman's side.
A trip to Ibrox is next on the agenda and Speirs is keen to see an improvement from his players.
He said: "I thought we were poor in the first half and hopefully we can learn from our performance.
"We are usually on the front foot yet too many times we passed the ball back the way.
"But the boys have been great so far and there is no doubt we are determined to finish as high up this league as possible.
"We can now prepare for the big match next week."