Dortmund beat Arsene Wenger's side 2-1 when the two sides met at the Emirates two weeks ago leaving three sides - Arsenal, Dortmund and Napoli all on six points in Group F.
And Giroud acknowledges that they cannot afford any more slip-ups if they are to progress to the knockout stages - especially at the Westfalen Stadion where no English club has ever won.
"We need to bring at least one point from here, from Dortmund, we know it," he told Sky Sports.
"But we knew from the start that it could be a tough group and we will have to fight until the last game. We need at least one point today and after a win at home against Marseille and after we will see, Napoli will be a crazy game maybe."
Giroud scored just 17 goals during his first year at Arsenal but has already scored more than half as many in the first 16 games of this season.
The France international has outlined the reasons behind his own improved form and is now hoping to steer clear of injuries as Arsenal look to continue their impressive start to the season.
"I'm OK with my body - physically I feel really well," he said.
"The big difference with last season is the confidence, and maybe I've improved myself in a technical way.
"The boss told me that, because we work a lot on it at the training ground. For me, it's all about focus and confidence.
"I had a really good pre-season with the team. I did not have the same last year.
"I have felt so good since the beginning. I have scored a lot of goals and it was really good for my confidence. I touch some wood, like we say, and, hopefully, I will not get injured.
"But if you look at my stats, I used to play a lot of games every season with not a lot of injuries so, hopefully, it will be the same this year as well."
Jack Wilshere will miss the game because of injury - he was unable to train on Tuesday and he did not fly out with the rest of the Arsenal squad to Germany.
Wilshere, whose last appearance for Arsenal was as a 69th minute substitute in the 2-0 away victory over Crystal Palace, is understood to be suffering from a problem with his left ankle that he picked up last week.
Arsenal manager Arsene Wenger said: "Jack Wilshere has not travelled. He has another test on Thursday. If he does not pass that he is out for Sunday and for England."
Theo Walcott is also out - despite widespread reports that he has stepped up his recovery in the last couple of days but could be available for Arsenal's Super Sunday clash with Manchester United.
However, defender Kieran Gibbs has given Wenger a timely boost ahead of the game, after taking a full part in Tuesday morning's training session.
Gibbs sustained a calf injury in Saturday's 2-0 victory over Liverpool, forcing him to be replaced by Belgium international Thomas Vermaelen after 76 minutes.
Watch Dortmund v Arsenal live on Sky Sports 1 from 6pm on Wednesday.