Steven Pienaar's goal proved the decider in a game in which Kevin Mirallas had seen his early strike cancelled out by Yannick Sagbo.
The Tigers boss was unhappy with Mirallas' opener which saw Gareth Barry coming back from an offside position and appear to get the slightest of touches to the ball on its way past Allan McGregor.
"It was close and it could have gone either way, but I have to say the big decisions went Everton's way," Bruce told Sky Sports.
"We had enough chances to take it, but we needed some decisions to go our way.
"With their first goal, Gareth Barry is standing in an offside position and for me he touches it and moves the ball. I think that's why it's gone in the net. If he's not interfering with it, I don't know what is.
"He knows he touched it and he's standing in an offside position. Even if he doesn't touch it, he is interfering because our goalkeeper thinks it's going wide, so he's standing in a position where he should be flagged in my opinion.
"And then Barry's two challenges - the first on Danny Graham - and the second one in particular on (Sone) Aluko is over the top. Those big decisions have gone against us."
Graham was caught by a high tackle from Barry and departed on a stretcher.
Bruce says he is keeping his fingers crossed for the 28-year-old, who is on loan from Sunderland.
"He's on crutches at the moment," said Bruce. "We'll have to obviously wait because we sent him for an X-ray, so we won't know the results until Monday or Tuesday at the latest."