The midfielder scored against Olympiakos on Tuesday night but it was to no avail as Arsene Wenger's side surrendered the lead to lose 2-1 in Greece.
Defeat followed the weekend loss in the Premier League to Swansea City, when fans at Emirates Stadium did not hold back in letting their feelings be known.
Arsenal will therefore have to try and win back the respect of their followers when they host West Bromwich Albion on Saturday and Rosicky thinks the current volatile atmosphere is damaging.
The Czech said in the Evening Standard: "I can understand the frustrations, I am an Arsenal fan as well when I am not playing.
"It is understandable but we have some young guys and this is not helping. We have to all stick together, which is what we did last season when everyone was writing us off.
"The performances we produced against Tottenham and AC Milan [in last season's Champions League], you could feel the great atmosphere at the Emirates. Without doubt that was the best atmosphere I have ever played in.
"We have to win the people again, that is the challenge. It will be difficult but we are capable of doing it again. If we are all on board, Arsenal is a great place to play football."
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