The Welsh capital region are five points behind sixth-placed Ulster following their 15-10 defeat by Scarlets on New Year's Day.
Fifth-placed Warriors are nine points ahead of the Blues in fifth.
"We have to get a win up there. If we don't then that top six is slowly slipping away," Warburton said.
"There will be a big emphasis on going up there, putting a lot of pressure on ourselves to produce a big performance.
"Otherwise it is going to be extremely difficult and we will be playing catch-up again."
The top four teams in the Pro12 at the end of the season play-off for the championship.
A top-six finish would also probably secure a place in the European Champions Cup in 2017-18 - Scarlets were the only Welsh region to qualify for this season's tournament.
Head coach Danny Wilson said the Blues missed an opportunity to win at Parc y Scarlets with home coach Wayne Pivac admitting his team were "hanging on a bit" at the end of the game.
The losing bonus point was little consolation for Warburton, who captained the Blues in the absence of injured prop Gethin Jenkins.
The fight for a top four spot will be a motivation for Blues against Glasgow, who completed a European Champions Cup double over Racing 92 in December.
"It is extra motivation because we know if we lose any more than two or three more games we are going to find it extremely difficult to get into that top six," Warburton added.
"There is pressure on all our games now, we have been decent at home, but away is where we have to improve.
"We had a good win away at Munster at the start of the season, but if we want to want to be top six then you have to go to a quality team like Glasgow and pick up wins.
"We have made good signings, from a playing and coaching perspective, and we really need to kick on to that next level and get in that top six.
"It is a huge motivation for the players."
Sam Warburton believes Cardiff Blues have to win at Glasgow Warriors on Saturday to keep alive their hopes of a top six finish in the Pro12.