Marouane Fellaini opened the scoring for United against his former club in the 34th minute before David de Gea produced a fine save down to his right to prevent Romelu Lukaku from levelling matters from the penalty spot 12 minutes after half-time following Timothy Fosu-Mensah's foul on Ross Barkley.
Everton did equalise 15 minutes from the end when Chris Smalling put the ball into his own net but Anthony Martial's cool finish in the third additional minute ensured there would be no extra half-hour or a penalty shoot-out, sending United into their first FA Cup final since 2007.
Roberto Martinez's men had chances to win the game themselves, but Van Gaal felt Everton's second-half revival was predominantly down to the decisions of Taylor.
The Dutchman told BBC Sport: "It's fantastic, when you see the joy in the eyes of the players, fantastic to see but also for the fans.
"I think we deserved to go in the final. I think the referee, we didn't have any foul in our benefit. He changed the match I think.
"We had so many chances, we could have finished it much earlier.
"They (Everton) came in the match because they get all the fouls, all the fouls around the 60 metre area, then the fans of Everton were cheering. In the first half and before that, no (they were not).
"The referees are deciding the game and not the players anymore."