Dan Ndoye's first international goal appeared to have Switzerland set for a famous victory on Sunday, only for Niclas Fullkrug to deliver a 92nd-minute leveller in Frankfurt.
That late intervention from the Germany substitute salvaged top spot for Julian Nagelsmann's hosts, though Switzerland also progressed through to the last 16 in second place at Euro 2024.
Xhaka believes his side can take confidence from the showing, with Germany scrambling at times and almost suffering an unlikely defeat.
"I think when you see the Germans celebrating, we can be proud of ourselves," Xhaka told reporters after the game. "It's not always easy against a team like that.
"Nevertheless, the late equaliser hurts. We said to ourselves that we have our own challenge. It started today.
"Of course, you have to compliment the opponent too. But above all, we have to be proud of ourselves.
"Everyone fought for each other and ran for each other. We always said that it had to be a very good day. We have to push ourselves to the limit. Then we can beat anyone."
Veteran midfielder Toni Kroos lavished praise on the Swiss but insists Germany performed well.
"It's clear that Switzerland are a good team," he said. "That's why I think we controlled it very well... In the second half, it got better.
"I think we improved in the second half. We played a little better there. But I'm totally satisfied with the team."
Germany captain Ilkay Gundogan was far less convincing in his praise as Nagelsmann's men missed the chance to make it three wins in as many group games.
"Of course, we would have liked to win the game and to play great football," the Barcelona midfielder said.
"But I think you also need games like that during a tournament. And that can also be a real strength for the next games, hopefully."
Germany will face second place in Group D in the last 16, while Switzerland's top-two finish sets up a meeting with the runners-up of Group B.
Xhaka looked set for the exit after he was stripped of the captaincy in November for reacting angrily to supporters who jeered him when he was substituted during a 2-2 draw with Crystal Palace the previous month.
The 27-year-old was also dropped from the squad for five matches, but he won back his place and, eight months on, is a regular member of the starting line-up again.
Arteta last week praised Xhaka for winning over the fanbase with his displays on the field, but the former Borussia Monchengladbach star admitted he seriously contemplated leaving.
"Everyone knows what happened with me and the fans - or the fans with me. It was not a good time. It was not a nice time," he told BT Sport.
"But maybe it was the key because I came back stronger than ever, so I learned a lot from this situation. I hope the fans have too.
"I was always saying to myself, but to the fans too, I am a guy that will go 100 per cent each game. The people start to understand me more and more now again.
"I have to be honest, I'm very honest with everyone. I was very, very close to leaving the club. I had, until this moment, had a great, great time in this football club.
"But after this, I was of course a bit down because I did not expect that from the people, from the fans.
"It was never in my mind to leave the club before, but after this happened, of course you think about it."
Switzerland international Xhaka has credited Arteta, who succeeded Unai Emery a little under two months after the incident, for turning around his career in north London.
"When Mikel arrived, I had a very good meeting with him, very good conversations," he said.
"Mikel was the guy. He turned me around and gave me a second chance, and he showed me he trusted me and I have tried to give him everything back."
Arsenal take on Chelsea in the FA Cup final on Saturday with Arteta seeking his first piece of silverware in management.
And after picking up victories over the likes of Manchester City and Liverpool in the past few weeks, Xhaka has praised the Spaniard for improving the team's fortunes.
"Since Mikel came to this club a lot of things have changed," he said. "He has changed the mentality, the spirit, not only for us players, but in the group.
"Everyone knows exactly what their job is. We have a clear gameplan.
"He prepared us really well against a lot of good teams and yeah, at the moment, it's like we are back with happiness. Coming to training with happiness, we do amazing work."
