Head coach Gregor Townsend is sure Glasgow are capable of holding on to a top two place in the Pro12 to make sure of a home draw in the play-offs.
Friday's 51-24 win over Munster moved Glasgow top of the table, with three league matches remaining.
"The players have a real belief about what they are doing," Townsend told BBC Scotland.
"If we win one or two we should be top four. If we win them all that will keep us in the top two."
Closest rivals Leinster and Ulster meet on Saturday in Dublin, while Glasgow will have a two-week break as the Heineken Cup resumes before a trip to Scarlets on 12 April.
A home game with Ospreys follows and the league campaign ends with a visit to Connacht.
"The play-offs was the aim at the start of the season," continued Townsend, who is enjoying a great debut term with the Warriors.
"We need to really prepare well.
"Scarlets play differently to a number of teams and have a very strong defence so it'll be extremely tough.
"But I believe with the way the players are playing and the effort they are going to put in in training over the next 10 days when they come back from their holidays, we'll have a good chance of winning down there."
Stand-off Ruaridh Jackson turned in a great all-round display to rack up 22 of the home side's points against a Munster side battling for fourth place and still involved in the Heineken Cup.
"We didn't deserve to be leading at half-time," Townsend conceded. "Munster could have been 10 points ahead.
"They were the better team, they showed more energy, more aggression and that was disappointing.
"We wanted a reaction in the second half and we got it."
Three of Glasgow's six tries were from interceptions from Sean Maitland, Niko Matawalu and John Barclay and Townsend was full of praise for the openside flanker.
"The first try was a great read by Sean Maitland and Niko's was an opportunist score," he said.
"Barclay's running lines were excellent, he worked well with Ruaridh and he picks his lines very well. His timing was good so he's always at pace when he takes the ball and I thought that was his best game of the season.
"You've got to remember he's had a number of injuries.
"John is back to the form he showed when he was playing for Scotland. He scored a cracking try against Castres in the Heineken Cup but did his hamstring, so he wasn't fit enough for the start of the Six Nations, but I'm really pleased for him."