Ralf Rangnick said it was "incredible" that Middlesbrough's goal was allowed to stand as they knocked Manchester United out of the FA Cup on Friday.
The Championship side triumphed on penalties at Old Trafford after holding United to a 1-1 draw, Matt Crooks cancelling out Jadon Sancho's opener despite the ball striking Duncan Watmore's hand in the build-up.
The Red Devils were punished for missing a hatful of chances as they failed to win a home FA Cup match against a lower-league side for just the fourth time in the past 32 such meetings.
After Cristiano Ronaldo had missed an earlier penalty, a deflected Sancho strike put United in front, but they failed to build on that advantage despite dominating proceedings in the first half especially.
Overall, United had 30 shots, the most of any team in a single FA Cup match since the start of last season, finishing with 4.32 expected goals to Middlesbrough's 1.43.
Yet they found themselves level when Crooks turned in Watmore's lob, the goal allowed to stand after Watmore's clear handball was deemed to be accidental.
United continued to be profligate, Bruno Fernandes somehow hitting the post with the goal at his mercy and Anthony Elanga heading a clear chance straight at goalkeeper Joe Lumley.
It was teenager Elanga who missed the crucial kick in the shoot-out, firing his effort over the bar after the first 15 penalties had been scored.
United have now lost six of their past seven shoot-outs in all competitions and the Champions League is now their remaining faint hope of silverware for this season given they are 19 points off the Premier League pace set by Manchester City.
"In the end, the goal should never have been given. It's incredible that it stood," Rangnick told MUTV.
"It was a clear handball. I would not have needed VAR, it should have been seen by the referee himself but the VAR should not have given the goal.
"As far as I know, the referee and the VAR said it was not intentional, it was coincidental, how can it be coincidental if the hand is up there and he controlled the ball with his hand?"
Despite his frustration with the equaliser, Rangnick admitted United only had themselves to blame for their cup exit.
"We're really disappointed," he said. "The players, the staff, everybody. This was completely unnecessary. We should have killed off the game in the first half. We could easily have been 3-0 or 4-0 [up].
"We started well and played extremely well in the whole first half. Our movement and tempo of the game were exactly what we intended to do. But it was only 1-0 and a goal like this can always happen, although it shouldn't have happened from our perspective because we didn't defend well, we were too open in that counter-attack situation."
Boro boss Chris Wilder conceded he had expected Crooks' goal to be disallowed at first.
"We rode our luck and took our chances," he told ITV. "The decisions that are made through VAR have changed since I left the Premier League. I thought straight away it was handball. I thought it would be chalked off and [I am] delighted it wasn't.
"The FA Cup is alive and kicking, especially in Middlesbrough. I told the players it was all about making memories."