Head coach Gregor Townsend says Glasgow are braced for "arguably the biggest game in our history" as they look for revenge against Toulouse next Saturday.
The four-time European champions moved top of Champions Cup Pool Four with a 19-11 win, with the Warriors paying for two yellow cards.
"We realise what a big game this is," Townsend said of the return fixture.
"They'll be tired and sore as well but we've got them at home and I'm sure it will be a sell-out."
Glasgow have never qualified from the group stage in Europe's premier contest but went to the Stade Ernest-Wallon leading the standings after opening wins over Bath and Montpellier.
Now they trail by three points and may need to find a way to beat a resolute Toulouse at Scotstoun to have a chance of reaching the quarter-finals.
Glasgow started strongly in Midi-Pyrenees but could not take advantage of their best spell.
"I felt that for a lot of the first half we were in control of the game, we just weren't able to put points on the board," Townsend told BBC Scotland.
"Their defence was excellent, so we need to look at ways to break that down better.
"The game at the highest level is about the small details, taking your opportunities and making the opposition have to execute for everything."
Toulouse added a converted try to their 9-3 half-time lead in the opening minutes of the second period, with Glasgow still down a man following Finn Russell's sin-binning for a dangerous tackle.
Leone Nakawara's yellow card cost the Warriors further, as did Duncan Weir's missed conversion effort which would have given them a losing bonus point after Niko Matawalu's late score.
"Probably the most disappointing aspect of the game was how we gave them a try right at the start of the second half from our turnover," explained Townsend.
"It was poor set-up, we didn't pass to the right player and clear the right man. But we defended very well for the other 79 minutes."
With the Toulouse pack impressive, Glasgow can take credit from their bravery but will need to keep fifteen players on the pitch next week.
"To be down to 14 men against a team that was on fire in periods for 20 minutes and still be looking like we could get a losing bonus point at the end was a great effort," said Townsend.
"Two yellow cards puts you under an awful lot of pressure against a team like Toulouse, who are offloading all over the place.
"Coming away from home against one of the best teams in Europe, it's tough to win with two yellow cards and a penalty count of 14 to five."
Full-back Stuart Hogg is looking forward to having another crack at the famous French side in six days time.
"We get to play them again next week and we'll learn from this," the 22-year-old said.
"I know Gregor won't be pleased with the penalty count. We pride ourselves on our discipline and we're pretty disappointed.
"We're a team on the up and we firmly believe we could have won that game, so hopefully we'll do them over next weekend."