Oli McBurnie's second-half goal earned Sheffield United a 1-0 home victory over West Ham United to move them up to fifth place in the Premier League on Friday.
Chris Wilder's side should have increased their lead but had to survive some anxious moments as West Ham's Sebastien Haller had a goal ruled out for offside and keeper Dean Henderson made a couple of sharp saves before the dramatic VAR intervention.
"We're fuming, we're livid," Rice said. "It's tough to take. He knocked the ball into my hand. There was no intention, it's a real kick in the teeth. I think it's the thought of every Premier League player, we don't want to have VAR in the game."
While West Ham, who lost keeper Lukasz Fabianski to injury early on, could feel hard done by, while Sheffield United would have been kicking themselves if they had not won after failing to kill off the visitors having taken the lead.
"We got a decision but we have had two or three against us this season," Wilder, who just signed a new deal with the team through 2024. "We dodged a bullet late on but I thought we were in control in the second half.
"It's a huge three points for us."
Sheffield United moved up three places into fifth with 32 points from 22 games, four points behind fourth-placed Chelsea.
It was a first loss for West Ham since David Moyes returned for a second stint in charge after Manuel Pellegrini was sacked on Dec. 28 following defeat by Leicester City and he was given his first taste of VAR disappointment.
"First of all I thought my players were terrific. We didn't deserve to lose," said Moyes, who looked incredulous at the VAR decision. "We were worth at least a draw.
"It was a good goal. Anybody who has played football or been around the game knows it was a good goal. Declan Rice did really good to break through the middle.
"From my point of view and the people who watch football, the decision is not right. Whoever was checking it got it wrong. I saw nothing wrong with it at all."
West Ham remain in trouble in 16th place, two points above the bottom three.