Healy appeared to have rescued a point when Boro keeper Mark Schwarzer failed to hold his injury-time strike with replays showing the ball had clearly crossed the line.
But referee Andy D'Urso and linesman Ian Gosling refused to award the effort, leaving Sanchez furious that their blunder had cost his side a point.
He said: "Everybody in the stadium saw as soon as it happened that the ball was over the line.
"It's a big decision that the linesman has to get right. He had a clear view of it.
"If referees and linesmen don't want technology to take the big decisions out of their hands then they have to make those big calls.
"Look at the reaction of the Boro players - their body language told them it was a goal.
"Plus five Fulham players jumped in the air when it went in. I told the referee a major error had been made between himself and the linesman.
"I can't understand how they didn't see it. I don't like technology; referees should be making the decision. But they have to be right."