The Gunners took the lead against Burnley on Saturday after Pierre-Emerick Aubameyang struck inside six minutes.
Arsenal dominated proceedings after that and should have extended their lead, however they failed to take their chances.
In the end, Burnley hit back before the break as Chris Wood intercepted Granit Xhaka’s pass from inside his own box to level the game.
Arsenal pressed for a winner after that and hit the post, as well as having a good shout for penalty turned down, but they couldn’t find a breakthrough.
It left them leaving Turf Moor frustrated, none more so than Chambers - who was making his top-flight appearance since December 2019 after recovering from a serious knee injury.
“It’s a bittersweet moment to be honest,” said Chambers.
“It was great to be back out there with the boys, it’s been a long time for me in the Premier League.
“So personally it’s good to be back out there, but unfortunately it’s not the result that I wanted to get today.
“I think we deserved more out of the game, we were pushing well towards the end and on another day, one of those chances drops in for us. So we’re all very disappointed.”
Arsenal are now 10th in the Premier League and any hopes of Champions League qualification by finishing in the top four have all but gone.
They can, however, still return to Europe’s premier club competition by winning this season’s Europa League.
Arsenal face Olympiacos in the last-16, with the first leg in Athens on Thursday, and Chambers has urged his team-mates to respond following Saturday’s disappointing draw at Burnley.
“It’s going to be about how we react and move onto the next game,”Chambers told Arsenal Media.
“We played the way we wanted to play for a large majority of the game. When you come to a place like this, you don’t want to get sucked into the way they play, because they’re very good at it.
“So it’s important that you stamp your authority on the game and that we play our style. I think we did that for large chunks of the game but unfortunately we didn’t get the result.”