Arsenal missed out on the chance to secure seeding for the knockout stages of the Champions League when they went down 2-1 at Olympiacos, where Czech winger Rosicky had fired the much-changed visitors ahead just before half-time.
The defeat extended Arsenal's winless run to four games, with Saturday's 2-0 home defeat by Swansea seeing Arsene Wenger's men plummet down the Barclays Premier League table to 10th place.
There has been plenty of tension on the terraces at the Emirates Stadium, which seems to be filtering through to performances on the pitch as the players fail to produce the required tempo.
Rosicky, though, has every confidence things can soon be put right - starting with the visit of West Brom on Saturday.
"I can understand the frustrations, I am an Arsenal fan as well when I was not playing," said Rosicky, who has just returned to action after being sidelined since aggravating his Achilles problem ahead of the European Championships.
"It is understandable, but also on the other side we have some young guys as well and this is definitely not helping them.
"We have to all stick together, which is what we did last season when everyone was writing us off and we came back stronger.
"You could feel the great atmosphere we created at the Emirates with performances against Tottenham and AC Milan [in last season's Champions League].
"I have been in professional football for a very long time and that was without any doubt the best atmosphere I have ever played in.
"Of course we have to win the people again, that is the challenge.
"It will be difficult, there is no doubt about that, we are capable of doing it again.
"If we are all on board, Arsenal is a great place to play football, but we have to stick together and fight."
Francis Coquelin came into a side last night which also saw European debuts for 20-year-old defender Jernade Meade and 18-year-old Swiss defender Martin Angha, who came on as a substitute.
The midfielder maintains the team cannot dwell on what went wrong in Athens, with the home side hitting back after a much-improved second-half display in front of their vocal support at the Georgios Karaiskakis Stadium.
"It is a tough place, but let's not forget we are Arsenal Football Club and when you come here, everyone wants to win [against you], we could have come back with a win so we are very frustrated," Coquelin told Arsenal Player.
"But now we have to concentrate on the next game, we have a really important match against West Brom and we want to get the three points.
"We had a few bad results recently, so we need the three points at the weekend."
Had Arsenal held on for victory in Athens, they would have ended up top of Group B as leaders Schalke were held to a draw at bottom club Montpellier.
As a result, the Gunners will not have the safeguard of avoiding one of Europe's leading sides, with the likes of Barcelona, Paris St Germain, Borussia Dortmund and probably last season's runners-up Bayern Munich all potential opponents in the last 16.
Wenger, though, maintains he is not overly concerned, stressing things could look very different for Arsenal when they return to European action in mid-February.
He said: "We have to wait for the draw, but we wanted to finish first.
"Some teams can get stronger until then, including ourselves."
Wenger is likely to recall his first-team regulars against the Baggies, with Theo Walcott, Jack Wilshere, Lukas Podolski and Olivier Giroud among those left in London this week.