Second-half goals from Atsuto Uchida, Kevin-Prince Boateng and Julian Draxler were enough to secure a comfortable victory for the German side, leaving Keller thoroughly satisfied at his team's opening performance in Group E.
He said: "We have managed a perfect start to our Champions League season.
"I’m extremely happy we kept our third consecutive clean sheet."
The result means that Schalke have now lost just one of their last 11 matches in the competition, and was no less than the home side deserved after a dominant start.
"We played well in the first 30 minutes, where we built a lot of pressure and created one or two chances," Keller added.
Steaua looked more lively after the break, but they could not convert a flurry of chances that came their way in the early stages of the second half.
Schalke duly took advantage, finding the net three times in the last half an hour.
And Keller was pleased with the way that they managed to kill off the game, adding: "From the 60th minute, we clearly dominated the game and then got some good goals.
"I am proud of the team."
Schalke now sit at the top of Group E on goal difference, level of points with Basel, who secured a surprise 2-1 win over Chelsea at Stamford Bridge.
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