The Spiders just lost out against Ally McCoist's side at the weekend.
A late Lawrence Shankland miss proved costly when Fraser Aird snatched the win in the last minute.
Next up for Queen's is the home clash with Clyde this afternoon as they look for a rapid response.
Manager Speirs said: "I had every confidence Lawrence would score, but he didn't manage to finish it off. He is 17, Aidan Connelly is 17 and there are another two or three who are 18 or 19 so they are only going to benefit from this."
Clyde head into the Irn-Bru Third Division clash on the back of a weekend win against Berwick Rangers.
Boss Jim Duffy said: "I have said that Queen's Park are a terrific side.
"Everyone knows how they play, they are a very good passing side and they have got width and pace.
"They are a terrific team so we will not underestimate the challenge of going there."