Schalke, who have lost two and drawn one game so far in the league, ended the match with nine men as captain Benedikt Hoewedes and Christian Fuchs were sent off in the 14th and 85th minutes respectively.
Confidence has hit an early low with the Champions League playoff second leg at Greece's PAOK looming next week.
"One could see that the team is functioning," Keller told reporters. "After a tough game on Wednesday (1-1 draw against PAOK) and with such warm temperatures to play with a player less for more than an hour to keep the game open shows character."
The way the team performed after the break was impressive, he said, after Adam Szalai cut Hanover's 2-0 lead and came close to an equaliser.
However, Keller, who came in late last year and saw his contract renewed after he helped Schalke clinch fourth place last season, is running out of options.
A string of injuries has not helped his case, with Jefferson Farfan missing on Saturday with an ankle injury and striker Klaas-Jan Huntelaar out for several more weeks.
For next week's game in Greece, Keller could also be without Joel Matip.
"What team?" he said, when asked about how he would prepare his squad for next week's European encounter that could take them into the Champions League group stage.
"Matip injured himself today, and as for Jermaine Jones and Leon Goretzka, I do not know yet. Our situation is not comfortable at the moment but we have what it takes to go there and win."
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- Christian Fuchs