The pair raced side-by-side and nose-to-tail in the searing heat, with Perez kicking up dust as he ran wide while trying to force a way past and making contact with the rear of Button's car.
Button, who ended up 10th while Perez finished sixth in the fourth race of the Formula One season, was not amused after urging his team over the radio to calm down the Mexican.
"There was a lot of clean racing, which was good – apart from with my team-mate," the 2009 world champion told reporters at the Sakhir circuit.
"Wheel banging at 300 kilometres an hour isn't normally the way I go racing, but there you go. It's great for the team that he got some points, but he didn't go about it in a very clean way I would say."
The 33-year-old Briton, who previously had 2008 champion and compatriot Lewis Hamilton as his team-mate and who is also the most experienced driver in the sport, said 23-year-old Perez had some growing up to do.
The Mexican came into the Bahrain weekend feeling some pressure after being criticised for the aggressive way he defended his position in China.
He had been told before that by team principal Martin Whitmarsh to use his 'elbows' more, and make life tougher for rivals on the track. Button clearly felt Perez had gone too far in that direction.
"I've raced with many team-mates over the years, and I had quite an aggressive team mate in Lewis," he said.
"But I'm not used to driving along a straight and having a team-mate coming alongside me and wiggling his wheels at me, and banging wheels at 300 kph. That's things you do in karting, and normally you grow out of it, but that's obviously not the case with Checo," added the Briton.
"Soon something serious will happen, so he has to calm down..I've had some tough fights in F1, but not quite as dirty as that."
Perez said it had been an equal, if risky, battle.
"It was definitely a bit too much. A bit too risky what Jenson and I did," he told reporters.
"I agree we were too aggressive. But he was as aggressive as I was as I went off the track a few times...It's something we have to talk about between us to sort it out."
Whitmarsh, caught in the middle, dished out praise and criticism in equal measure.
"What you don't do is hit your team-mate from behind and potentially give him a puncture and potentially take your front wing off," he said. "So that was too far.
"But people have been saying he (Perez) hasn't had the spark this year. I think he definitely had the spark today. So overall, a fantastic fighting result.
"I think he'll come out of it with some confidence, he's a young driver and has got to learn and perhaps calm down a little bit in some things but it's that passion that got him past a few more drivers later in the race. So you don't want to extinguish the spark."