The Switzerland international was quite pleased with the outcome of Tuesday's match in Piraeus, but added that the team still has work to do.
Benedikt Howedes gave the Konigsblauen the lead in the opening 45 minutes of Tuesday's Group B curtain raiser, before Djamel Abdoun restored parity in the second half.
Klaas-Jan Huntelaar ensured the Germans claimed all three points with a calm finish, much to the satisfaction of Barnetta, who reflected on a "crazy" game in Piraeus.
"It's still very early in the competition to say what we can achieve," Barnetta told UEFA's official website. "We want to play at a high level consistently and take points. We have made an important step, but there is still a long way to go to achieving qualification.
"We did what we set out to do against Olympiakos: win the match in a very intense atmosphere. We managed to score the opener, then had a very good chance to make it 2-0 but didn't. Afterwards, they equalized. We took the lead again almost immediately, and then wasted a penalty. It was a crazy match, but we won and that's what matters."
Schalke locks horns with Montpellier on Oct. 3 in the club's second group game.
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