Going into the game having lost three of their opening four Group F fixtures, Wenger’s side needed to win by two goals or more at the Karaiskakis Stadium or better the 3-2 defeat they suffered at home to the Greek champions in September.

With seven key first-team players missing through injury, Giroud produced the goods when it mattered as Arsenal made light work of a seemingly difficult task to seal a 3-0 win.

Only seven sides in Champions League history had managed to progress from the group with three points or less after four games – but Arsenal have now added their name to an exclusive list and Wenger reckons it can have a lasting effect on his players.

“It will make us stronger and strengthen the belief of the squad,” he said.

“It is a special night for us because, as we said before the game, we were in escape mode.

“We needed something special and when you deliver something special it can create positive memories for the rest of the season. Maybe it’s a lucky year for us in the Champions League, you never know.

“I told you before the game it would be a great escape, and I must say I’m very proud of the team.”

Arsenal still have seven first-team players out injured but winning in such a convincing fashion without them gave Wenger extra satisfaction on what he admitted was a memorable night.

When asked whether it ranked as one of his best European wins, he replied: “Yes, certainly because we needed a perfect performance to score without conceding. That is not easy because Olympiacos are a good side.

“It is a fantastic achievement for us. When you look at who we’ve lost in the last three weeks, we’ve lost (Francis) Coquelin, (Santi) Cazorla and Alexis (Sanchez) among other long-term injuries.

“Not many people gave us a chance. We are a real team. In the dressing room this team is very close and you could see that again today.”

Arsenal could now face Andre Villas-Boas’ Zenit St Petersburg, Manchester United’s conquerors Wolfsburg or one of the Spanish trio of Real Madrid, Barcelona or Atletico Madrid in the next round.

Olympiacos head coach Marco Silva felt his side were left in a state of limbo after Giroud’s second goal meant they needed to score themselves to advance.

“We started strongly, we tried to create chances,” he said.

“It is true that at 2-0 we intended to take risks, to keep trying. We had the opportunities to score but our goal was at risk. The third goal killed our hopes and there ended the match. Whatever we did from that point we knew what it was too late.”