Although Arsenal, which had beaten Olympiacos in the UEFA Champions League earlier in the week, is currently just outside the top six and seven points off the pace, Giroud believes there is plenty more to come.
"We will keep going and stay confident for the future. I think we have a very interesting role in this championship," Giroud told Arsenal Player.
Giroud produced a neat close-range finish when turning in
Speaking to French broadcaster Canal+, Giroud added: "I expected it to be difficult at first because the Premier League is a level higher and I have had to adapt.
"It is nice to have scored my first goal, that will give me a lot of confidence for the future.
"I feel good about this team and I am confident that I will score more goals. Why not a dozen like in my first season at Montpellier?"
Podolski opened his Arsenal account in the 2-0 win at Liverpool before the last international break.
The German, signed from Cologne, feels Giroud can now play with more freedom when the domestic action begins again with a trip to
"Everybody wants goals from strikers and it was not easy for Olivier," Podolski told Arsenal Player.
"You must wait for your chance, keep fighting and the goals will come."
Arsenal could have
The 24-year-old spent some of last season on loan at Hull City, but played down as 'crazy' reports he was concerned over his long-term future with the Gunners.
Mannone, signed from Atalanta in 2005, told the club's official website, www.arsenal.com: "Neither myself nor anyone from my family or friends have spoken about any deal. At the moment I am really happy and just focusing on training and playing well.
"I am trying to be the number one for this club and win trophies, that is my only concern and I would like to make that clear.
"The boss has given me the chance. I have to keep going and prove myself in every single game.
"This is my best time at Arsenal so I would be crazy to not take the chance to put up a fight for my place.
"I am really happy and honoured to play for this club."
Arsenal will have nearly all of the first-team squad away on international duty.
Serge Gnabry and Chuba Akpom sealed a 2-0 win for the Gunners, with Wilshere playing a part in both goals.
The 20-year-old managed 74 minutes, Sagna completed an hour unscathed and Frimpong played the entire game.
English Premier League
Former England captain John Terry has insisted he has no plans to make himself available for 2014 FIFA World Cup selection.