Amid the euphoria of Arsenal’s Champions League progress at Olympiakos on Wednesday night, there was the underlying sense of reprieve; a feeling that the club had got away with it.

This was the footballing equivalent of Indiana Jones reaching back and grabbing his hat before the wall descends. At the very last moment Arsenal had found their focus. The standout line after the Olivier Giroud-inspired 3-0 win at the Georgios Karaiskakis Stadium, which squeezed Arsenal into the last 16 at the expense of Olympiakos on the head-to-head tie-break, came from Theo Walcott.

The forward looked ahead to Monday’s draw for the first knockout round and he remembered what had happened last season. After a rather more comfortable qualification Arsenal might have been drawn against Real or Atlético Madrid, Barcelona, Bayern Munich, Porto or Monaco in the last 16. To everybody’s relief they got Monaco – and Arsenal lost.

“Whoever we end up playing this time, we must respect them,” Walcott said. “Monaco, obviously … we didn’t respect them at all.”

If Arsenal did not respect Monaco – at all – it is no great leap to suggest they did not respect Dinamo Zagreb and Olympiakos when the draw was made for this season’s group stage. The club took their eye off the ball in the opening two ties, losing 2-1 in Zagreb and 3-2 at home to Olympiakos, and the requirement for what the manager, Arsène Wenger, described as the “greatest escape” on the final night in Athens was set in train.

Arsenal fashioned their lifeline with the home wins over Bayern and Dinamo, and they clutched it and hauled themselves to safety in Greece. It was a momentous occasion and to put it into some sort of context, it is worth noting that during the Wenger years the club have overturned a first-leg deficit only once in Uefa competition.

That was in 2009-10 when, after a 2-1 loss at Porto in the last-16, first leg, they won 5-0 in the return. It was still a group phase tie against Olympiakos but, because of the permutations, it had the trappings of a two-legged knockout.

Walcott talked about the “fantastic attitude” the team had shown with their backs to the wall and in extremely hostile surrounds. Unlike in Monaco last season, when they fought back to level on aggregate in the second leg, albeit with fewer away goals, they did not rush things at 1-0 up against Olympiakos. The performance was marked by icy cool.

The victory has the capacity to ignite Arsenal’s season, both at home and abroad. They have been determined to dig in during their injury crisis, to stay in touch, particularly in the Premier League, and, when everybody is fit, the hope is they can lengthen their stride. They showed what was possible with their fine form over the second half of last season.

Arsenal are not only through in Europe, they sit two points off the top of the domestic table. This, however, has to be a turning point, the moment when their mentality hardens into that of champions.

One thing is clear. They will not always qualify with three Champions League group stage defeats; playing fast and loose might sting them in the future.

“I think this result can lift our season,” Walcott said. “The amount of confidence in that dressing room is spreading out to all the players. That’s what you want going into the Christmas period because the Christmas period in the Premier League really maps out where you are going to be at the end of the season.”

Every one of the club’s 1,200 travelling supporters will remember Wednesday for a very long time. It was an occasion when everything came together and every last detail was, in Wenger’s opinion, “perfect”. Giroud was magnificent, completing his personal transformation from red-card villain in Zagreb to hat-trick hero, while even Wenger’s psychological tricks paid off.

He told the press on Tuesday night Olympiakos could be gripped by a “fear factor” if they fell behind because they would become painfully aware of what they stood to lose – which ensured that a message was sent out via the headlines. He then reinforced it to his players in the dressing room.

“That first goal was key, we just had to unsettle the fans,” Walcott said. “You could tell by the atmosphere here that they are a massive part of this team. Once we got them quiet and got them on the team’s back we knew we had the game won. The manager told us that at the start of it.

“It was one of the great European nights. We made it so difficult for ourselves, no one really gave us any chance but the attitude in that dressing room was fantastic. We knew what we had to do and we always felt that if we kept a clean sheet we would win. The great thing with this game compared to Monaco last season was that we were very patient with the buildup play. Even when we scored we didn’t go all-out attack. We were calm and relaxed because there was plenty of time.”

Arsenal will face one of Real, Atlético, Barcelona, Wolfsburg or Zenit St Petersburg in the last 16 and Walcott reflected the burgeoning confidence.

“I’m sure none of them would like to play us after this result,” Walcott said. “Whoever you get in the draw is going to be difficult. You’ve seen teams struggle when they should go through and should be winning. It’s the way the set-up is now. Even in the Premier League you see every team is getting much better.

“But it doesn’t matter who we get. If we all contribute and play like that then we can beat anyone on our day. If we get a few of our players back as well then our squad will be even stronger than it is now. I’d just like to make the job a bit easier next time.”