With Edouard Mendy sidelined with injury, Kepa was able to keep a clean-sheet in Sunday's derby win over Tottenham Hotspur.
"He seems happy to me, he may not be happy with the situation but he is happy with where he is at and the part he plays in the team," Tuchel said of Kepa.
"Everyone wants to play more minutes. We have contracts for 24 players including goalkeepers so we simply cannot give the same amount of minutes to everyone. It's the same for the guys who play on the field but it is more dramatic for goalkeepers. That's because we don't change them during games so maybe it seems even worse or harder.
"I don't feel Kepa like this. I feel an open guy, a humble guy, a super nice guy, a top, top professional sports guy who is a big part of this squad. I feel him happy. Maybe he could be even happier with more minutes but I don't feel him concerned at the moment because he is pushing and fighting for his chances.
"You can't force situations. I have a feeling with his mindset that he is here and he pushes with his calmness and positivity. He did not force it. He doesn't have to prove to me that he is a good goalkeeper because I see it every day in training. Maybe that's the point, that he does not try too hard to convince everybody that he is worth what the club paid.
"Who cares about what the club paid? So what. Money doesn't matter now. The question is whether we can afford to have him as a goalkeeper.
"We have two super strong goalkeepers. Do we need them both? We have proof last weekend. He was a key factor to have a clean sheet in the weekend. It is as easy as that. Whether the money is too high or low, these measurements don't matter to us. This pressure is off his shoulders and he deserves it to be off his shoulders so it is not his fault."
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