Referee, Michael Oliver awarded a penalty to the visitors after Bruno seemed to catch striker Dominic Calvert-Lewin in the neck with his elbow.
The Seagulls had led through Anthony Knockaert's first Premier League goal before Everton's Wayne Rooney stepped up to deny Brighton a third successive home win.
The score draw leaves the pair on level points and only three points above 18th place Leicester City who play West Bromwich Albion tomorrow.
Right at the death
Bruno said: "To get a point against Everton is good, but after being 1-0 up with five minutes to go it's quite disappointing. Especially the way with the penalty.
"I would say it wasn't. I haven't seen it again. I'm trying to put myself in the space. I'm not going to speak about the ref. That isn't fair."
Bruno feels hard done by
Bruno believes on another day the decision may have gone the other way.
He added: "They (the officials) are trying to do their best. I think it was really soft, every single decision during the game.
"There were a lot of challenges in the game and it was his decision, that's it."
The Seagulls' next game is away to West Ham on Friday and will be looking to build upon their impressive debut season.