The Spiders turned in an impressive showing at Ibrox last weekend but saw Ally McCoist's side claim top spot as a Lee McCulloch double clinched a 2-0 win for the Light Blues.
Next on the agenda for Speirs' side is a Hampden clash with Berwick Rangers, with the Borderers one of a host of sides aiming to put together a solid run of form to put them-selves in promotion contention.
Queen's have been in superb early-season form and Speirs is keen for his players to once again hit top gear when they star at the National Stadium.
He said: "It is another difficult game for us.
"Our matches with Berwick are always close and they are always difficult games.
"We know that we will have to play very well if we are to win the game.
"We will take the positives out of the Rangers game, there were certainly a few. It is about looking forward for us now and the next game is the most important one.
"We know that we will face a difficult game against Berwick, but we want to get back to winning ways.
"There is the chance to go top of the league.
"After Saturday, that will be the first quarter of the season finished.
"I don't think the league has settled down yet. It will be another quarter before it settles down a bit.
"In the meantime, we just have to concentrate one game at a time and try and pick up as many points as we can and hopefully, as we progress through the season, we can remain in a good position."