The 32-year-old has just come back from a frustrating spell on the sidelines following an Achilles injury which was aggravated at Euro 2012, and his well-executed goal fired the Gunners into a half-time lead at Olympiacos on Tuesday night.
Rosicky, though, was taken off at the break in a pre-planned move to protect his fitness, with a much-changed Arsenal side going on to lose 2-1 as they missed the chance to finish top of Champions League Group B and so secure top-seeding for the knockout stage draw.
It was a fourth match without a win for Arsene Wenger's team, who find themselves down in 10th place in the Premier League table after last weekend's 2-0 home defeat to Swansea.
Rosicky, however, feels his quick-passing game can raise the side's tempo which has been faltering badly in recent performances, as they prepare to tackle West Brom at Emirates Stadium on Saturday.
"It has been a long time out for me, so I hopefully I can build something on this and do a lot for the team again," said the Czech captain.
"I hope I can show my true self again and I will do my best to help this great club to be better again.
"I am a creative player, that is where I can contribute, but it will not be easy for me to regain the match fitness, so let's see how it goes."
Rosicky continued: "Maybe I can also help bring calmness, because sometimes we do not keep the ball as much as we used to.
"We have some good players in this team and what we are producing now is simply not good enough, we know that and are not happy about it.
"You can see there are more back passes then we used to play, that is probably a matter of confidence as well.
"You can gain that confidence by training well, winning the next game, then it will come back again."
Rosicky knows Wenger's squad need to step up their final product if they are to overcome a West Brom team who, despite defeats last week, have made an impressive start to the season.
He added: "We will sort it out quickly and have another game on Saturday, which is a good opportunity for us to start all over again.
"As a team we are not in a good position, we have to stick together and all fight, that is the only way we can do it."
Rosicky captained the Czech Republic in their opening two matches at Euro 2012, but his tournament was cut short following an injury sustained against Greece.
The Arsenal midfielder admitted it had been a tough spell.
"For the position I play, I always have someone on my back when I receive the ball - how can I defend myself against that, when someone kicks you?" he said.
"I had taken a kick on my Achilles during the season, and they finished me off in the Euros.
"It is part of the game, you have to take it, but it is difficult for me."
Rosicky continued: "If you start to feel sorry for yourself, that is the worst thing you can do - you have to fight constantly, so that is what I do."
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, as youngsters Jernade Meade and Martin Angha both made their European debuts in Athens.