The Germans have won their last two games following the 4-2 loss at Old Trafford and will hope to make it three against Hannover in the Bundesliga on Saturday.
Leno believes the side's ability to recover mentally from a loss has improved significantly with recent victories against Mainz and Arminia Bielefeld.
"We don't get bummed out by those kind of games anymore (the loss to Manchester United)," Leno said.
"We always try to see the positive side and we have to learn from our wins but also from our defeats.
"That's what I mean about us being more mature; the team analyses these games and then simply forgets about it."
Sami Hyypia's men sit third on the Bundesliga table but opponents Hannover are enjoying a good start to the season and Leno has urged his teammates not to be complacent.
"(Hannover) didn't show their best away from home the last year but nevertheless they have a great team," Hyypia said.
"They are a highly dangerous team when it comes to counter attacks and set pieces and we have to be careful for the whole 90 minutes.
"A win would be great but we shouldn't make the mistake to underestimate Hannover."
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