The Japanese driver has qualified in the top 10 for the last three races, outpacing his more experienced team-mate Daniel Ricciardo.
He secured a seventh-place finish in Australia, helped by the retirements of Max Verstappen and Lewis Hamilton and a penalty for Fernando Alonso.
Tsunoda then followed up with 10th on merit at his home race in Suzuka, making up for a poor initial start by performing some spectacular passing moves and benefiting from a quick stop when a gaggle of cars pitted at the same time.
“He said he went out with the samurai spirit,” Bayer told Motorsport.com. “I think it was an amazing achievement for him in front of the home crowd and Honda.
“Somebody told me it is the first time [for a local driver] since 2012 when [Kamui] Kobayashi scored a point in a Japanese GP, so a great achievement from Yuki, honestly.
“It was an immaculate drive from him, and he was managing the tyres when he had to, he was pushing when he had to. He had great support from the team with that pitstop. Overall very, very happy with him."
Bayer said that Tsunoda soaked up the pressure of performing in front of his home crowd, reflecting an overall change in his approach this year.
“That's something that we've seen now at the last couple of races, and he has made such big progress mentally.
“Over the winter he made amazing progress physically, but mentally he is on a different level now.
“He's taking this up, and he's taking actually energy from it, rather than being distracted. I think this was certainly a mega drive from him."
Tsunoda has outqualifed Aston Martin’s Lance Stroll at every event so far this year. However, Bayer says that it’s too early to suggest that RB can continue to outpace the Canadian and infiltrate the tail-end of the group of top-five teams.
"I have to be careful with that,” he said. “Probably what helped us is that it seemed that initially, Lance didn't get as much out of their upgrade as we initially thought.
“And we have been a bit better here than we thought because we were actually thinking this is not a track for us. Also, our new upgrade is probably more aiming towards the coming races.
“But I have to say that the team is honestly so focused on finding that hundredth here, a tenth here. It's a massive effort where everyone's fighting for it.
“And I think that it's a homogeneous push, and that's probably what allows us to sort of sniff into the top 10.
“What we felt, and that's what we're proud of to a certain extent, this was the first time we are in the top 10 based on race craft, it's not because something happened, or someone messed up."
