The Clarets found themselves going a goal down just before half-time when Cole Palmer stuck away a controversial penalty.
Lorenz Assignon was sent off for the foul on Mykhailo Mudryk, earning a second yellow card despite making minimal contact with the Chelsea man.
Such was the fury of Vincent Kompany, the Burnley boss was also dismissed and shown a straight red for his remonstrations on the sidelines.
He will inevitably be feeling proud right now though after his Burnley side fought back not once, but twice with 10 men to draw 2-2 thanks to goals from Josh Cullen and Dara O’Shea.
“Incredible, incredible,” Bellamy said, sitting in for Kompany for the post-match press conference.
“How selfless they were able to play for each other, how demanding of each other they were…
“I know Chelsea haven’t quite got the points they would like this season, but they’re an outstanding team with outstanding footballers.
“To be able to show the patience they showed, working together, the organisation, the commitment, you couldn’t be nothing short of proud watching it.
“The manager is more defensively-minded than myself because of where I played, but he really enjoyed that. He’s really proud of it as well.”
So impressive were Burnley, they were the side that came closest to winning it late on when substitute Jay Rodriguez rattled the crossbar.
Bellamy added: “I felt we were in the game 11-vs-11. Every time we had the ball we felt we were able to do something.
“Maybe the final pass at times we would have liked to have been better, but every time we were in possession we were able to progress up the pitch and get in Chelsea’s penalty area.
“It was more just the final ball that could have been better at times but we felt we were able to do something here.
“Now out of possession, Chelsea went to a diamond so they were able to cause us a lot of problems. We tried to get a handle on that but if you watch the game back, especially in the first-half, it was end to end quite a lot. A lot of chances.
On the controversy of the penalty and Assignon’s dismissal, Bellamy kept his thoughts to himself.
“It’s really not my position to be able to talk about it. I feel the manager will be able to address that in the next couple of days,” he said.
“I’ve got to be honest, I’d feel quite uncomfortable talking about that, it’s not my concern.
