The Gunners are currently occupying second place in Group B but are just one point ahead of Olympiacos, who they will play away from home on the final match day.
After taking just one point from two fixtures with group leaders Schalke, Giroud believes that his side cannot afford to cede any more ground when they host bottom side Montpellier at the Emirates.
"It's a must-win match for us because Arsenal have to go through to the next phase of the competition," the French striker said in The Sun.
"Montpellier have nothing to lose now they are already eliminated but we have to be careful as that's when some teams are most dangerous.
"They didn't become champions of France with no talent. We must not take anything for granted when they come to the Emirates."
Giroud moved to Arsenal after winning the Ligue 1 title with Montpellier last season but has seen his old team struggle both domestically and in Europe during the current campaign.
He added: "I've spoken to some of the guys at Montpellier and they have been having a difficult season. It was a big surprise to everyone that we were champions of France and maybe it was hard to digest.
"Last season things seemed to go our way. We were riding a wave and it seems that wave isn't there anymore."