The Switzerland international was pleased with the outcome of Tuesday's match in Piraeus, but added that the team still have work to do if they are to progress from their group
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.
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Nevertheless, 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 equalised.
"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 lock horns with Montpellier on October 3 in their second group game.