The Trail Blazers were trailing by two points when Lillard's layup was blocked by Rudy Gobert with 13.5 seconds remaining in the fourth quarter, but the Jazz center's touch clearly came after the ball hit the backboard.
The three officials on the floor failed to make to make the call, though, and Utah went on to claim a 117-114 victory at Vivint Smart Home Arena.
Speaking to a pool reporter after the game, officiating crew chief Josh Tiven admitted a mistake had been made: "We've since looked at it via postgame video review, and unfortunately saw that we missed the play, and a goaltending violation should have been called."
Lillard was incensed and had to be held back after the buzzer, with his temper still running hot when reporters entered the locker room.
"We get to the last play until the game and they miss an easy call, then they tell us it's an easy no-call, like that was obviously not a goaltend. It cost us the f****** game, man," said Lillard, who finished with 42 points, six rebounds, six assists and two blocks.
"It's an easy call. Three referees out there and they don't call that. And I don't want to see no report about, 'Oh, we should've called it'. None of that. They cost us a game. We're in a playoff race and they cost us a game on an easy call.
"There's no way to take the sting out of it, we can't have the game back, they cost us a game. It's a loss on our record.
"We're in a playoff race and we need every game that we can get and we had that type of effort and they miss an easy call like that, and then you want us to walk away and say nothing? It cost us the game. Of course we're gonna have something to say about it, man, it's BS."
Shooting guard CJ McCollum suggested the officials need to be punished for the glaring error.
"The call they missed was very costly for us, it cost us the game, we can't get it back," said McCollum. "I just don't like the explanation I got, that really p***** me off.
"There's three of you [referees] out there so if one of you doesn't see it the other two are supposed to be in another position to see it, so for you to say, 'It wasn't even close', and one person to say, 'It might've been obvious to you but it wasn't to us', it makes me just think you're not capable of doing the job in the way you're supposed to do it, which means you should be reprimanded, you should be fined accordingly.
"When we make mistakes we're fined, and they cost us a game that could cost people money. So they should be fined accordingly, because that's terrible. Not just bad, terrible."
Portland coach Terry Stotts said: "It's just a shame it was decided on an inexcusable missed call, there's no other way to describe it. They could've called goaltending and reviewed it, but they swallowed their whistles on a play that was pretty obvious.
"It's disappointing that such a great effort was decided by that. Everybody's pretty p***** off. You would think they would get that one right. I don't complain about officiating - they've got a tough job - but a play like that is inexcusable."
Despite appearing to suggest it was not a goaltending violation by shaking his head as Lillard appealed to the referees in the immediate aftermath, Gobert acknowledged the on-court decision was incorrect.
"I was just trying to make a play on the ball, and obviously after watching the replay you can see that's a goaltend," he said. "I was just trying to make a play. Goaltending happens all the time, it's part of the game.
"It's what people are going to talk about, they're not going to talk about us coming back from 14 [points behind] at half-time and us playing well as a team and fighting to come back in the game.
"Obviously it's a big play because it's the last play and it's what everyone is going to remember, but I think we did a great job in the second half. Mistakes are made, officials are humans and I feel it's part of the game."
