The Whites were sent crashing out of the FA Cup at the third round stage for a fifth straight season.
David Moyes saw his Hammers outfit defeat their West Yorkshire visitors 2-0 at the London Stadium on Sunday afternoon.
The game, though, saw more VAR controversy as West Ham opened the scoring in the first half through Manuel Lanzini.
Nikola Vlasic barged his way into the box under pressure and saw a shot blocked before Jarrod Bowen ran across the goalkeeper's path in a scramble.
The ball then rebounded to Lanzini who crashed an effort home and gave the hosts the advantage.
Replays showed Bowen in an offside position when the initial shot was made ahead of a flurry of action with a second touch from Vlasic.
After a lengthy VAR review, the goal was awarded amid protests from Leeds.
Bowen then scored in added time at the end of the second half to seal passage into the fourth round for the Hammers.
"I actually thought it was offside. When we originally saw it in real time I thought great movement, great positioning," Beckford told ITV Sport of the controversial opener.
"But you see just as the connection is made to have a shot, which obviously is blocked, I feel Jarrod Bowen is in an offside position.
"He starts in an offside position and goes for it, [Illan] Meslier gets a touch on it and the ball falls to Lanzini. [It's a] lovely finish but you know when it was back to VAR I actually thought they were going to pull it back and, in my opinion, I think they should have done."
Fellow former striker and pundit Jermaine Defoe agreed with the ex Whites front man over his assessment.
He added: "When you slow it down and you can see he was in an offside position and he was on the move and went for the rebound so that's why when we watched it back we thought it definitely was going to be given offside.
"Lanzini follows in and it's a lovely finish. Just that fortune they needed at that stage of the game as there was not much in it before that."