By FOX SPORTS staff
The Bundesliga club got the proceedings underway with a 17th minute strike from Roman Neustadter, but subsequently took their feet off the pedal to allow Turkish duo Hamit Altintop and Burak Yilmaz to strike back before the break.
Going on an all-out attack in the second period, Schalke managed to level the game through Michel Batos. However, their vulnerabilities at the back ultimately cost them when Umut Bulut fired home an injury-time winner to secure Galatasaray a place in the last eight of the Champions League.
Keller was at a loss for words after the game, but he admitted that his team should have done better in the first period.
"I have no explanation for the first-half performance. We played like we were doing a couple of weeks ago, without the necessary aggression, and everyone put in maybe 10% less than what was needed. We were not proactive and focused enough – we allowed them too much space," Keller explained to uefa.com
"In the second half we dealt with them much better. They played with a diamond in midfield and that had surprised us. We then coped with the challenge much better."
Star striker Klaas-Jan Huntelaar was forced to sit out of the second leg after picking up a knee injury over the weekend. His manager conceded that Schalke could have done with the services of Huntelaar and his fellow forward Ciprian Marica.
"You must not forget that some of our players were sidelined today [Tuesday]," Keller pointed out.
"The second half was really strong and there is no reason to be depressed now."
Schalke midfielder Julian Draxler admitted his side were gutted to have exited the competition.
"It's very bitter because we were very unlucky to lose," said Draxler.
"I think the second half still confirmed the good progress we have been making in recent weeks and the team believed in it to the end."
Altintop, who previously played for Schalke, insisted his passionate celebration after scoring was not meant to be an affront to his former club but rather a duty towards his new club's supporters, who made up a large proportion of the crowd inside the Arena AufSchalke.
"Of course I am still a Schalke fan, even if nobody wants to believe me," he said.
"I now play for another club and the Galatasaray fans deserve my celebration and my passion, which I showed.
"I hope that doesn't mean the Schalke fans will be angry with me."
Schalke return to domestic action with a league fixture against Nuremberg on Saturday.