Coach Sean Lineen is looking for an even better performance than Sunday's win over Montpellier when Glasgow Warriors go to France for the return.
The Scots claimed their second win in three games in Heineken Cup Pool 3 by earning a 20-15 victory at Firhill.
"It was a fantastic win for us but as a coach you always want more," Lineen told BBC Scotland.
"The first half was frustrating. When you look at the number of line breaks we made, we only finished one off."
Second-place Warriors, on eight points, now trail Leinster by three but are two points ahead of Bath and four clear of Montpellier, who they play again on Saturday.
Progression to the quarter-finals of the Heineken Cup, a trophy contested by clubs from the top six countries in European rugby, remains a possibility. The six group winners and the two best runners-up advance to the last eight.
But, while delighted to have beaten the French Top 14 side, Lineen believes improvements must be made.
"The players are giving everything and the game plan was right," he said.
"The ambition is there. You can see what it means to the guys. They never gave up.
"But we need to look at how we get the ball to our backs. It's something we are working really hard on.
"We just need to keep the ball a bit longer. When we upped the tempo, when we kept the ball longer, that was when we had them under pressure, but there were individual errors - dropped balls."
Four penalties by Duncan Weir, one by Ruaridh Jackson and a try by Federico Aramburu had the Warriors in pole position as the match neared its conclusion.
But Sakiusa Matadigo scored a try on the right wing from a French break to earn the visitors a late consolation.
Looking ahead to the return match, Lineen said: "To give that bonus point away at the end makes us concentrate our minds on what's in store next week.
"I'm sure there will be a few changes in their team. You saw what they can do: they are dangerous.
"They scored that great try at the end. We were pushing the game a bit, we didn't really need to - a bit of naivety maybe.
"It takes a bit of gloss off, I suppose, but to win in the Heineken Cup is a great result."
The former Scotland international went on to praise the backing of the 5,287 crowd and insisted that the club is heading in the right direction.
He said: "The crowd really made a difference. The atmosphere was brilliant; that's what the players want to play in front of and winning certainly helps.
"I've been here a while now and it's just fantastic to see the momentum we are getting on and off the pitch and we are not finished yet.
"The game against Montpellier is really important for us. We'll get a good week's training, go across there on Friday, then it's the Edinburgh double, so it's a big month for us."