United moved into the quarter-finals of the FA Cup with their victory at Deepdale Stadium; coming from behind thanks to goals from Ander Herrera, Marouane Fellaini and Wayne Rooney.
Scott Laird put Preston in front in the 47th minute and Grayson claimed that goal could have won his side the match if a few referee decisions had gone their way.
The 45-year-old manager was particularly frustrated with Rooney's penalty, claiming Preston goalkeeper Thorsten Stuckmann did not even touch the United attacker before he went down in the box.
Grayson argued Rooney could have been judged offside in the lead-up to Herrera's goal, while he claimed Fellaini fouled a Preston defender before giving United the advantage.
"All three goals were slightly contentious," Grayson said after the match.
"I've seen them all and on another day, we could have had the decisions go our way.
"The first one, it's a grey area. Wayne Rooney is not directly in front of him but just to side.
"The second one, we felt Tom Clarke was pushed by Fellaini. The third one, Wayne Rooney was not touched by the goalkeeper.
"There was no contact. He got out of the way, he took evasive action.
"All three could have been quite different for us but those are the fine margins in football matches."
