In a tight game, the Storm emerged victorios by just five points following a last minute try to Will Warbrick, but it was the lead up to the try which had Melbourne fans briefly seeing red.
Klein, who was also guided by bunker referee Chris Butler, failed to blow a penalty on a high shot to Melbourne hooker Harry Grant, despite replays showing clear contact to his face.
After staying down, he was eventually ordered to play the ball, with Melbourne scoring off the next play, but Storm coach Craig Bellamy said he didn't want to sweep it under the carpet, questioning whether there were different rules in the finals.
"I didn't have a close look. The Harry one - he got hit high. Nearly every game this year it would have been a penalty," Bellamy said.
"If we get beaten by a point, I think we'd be talking more about it, but that said, I don't want to sweep it under the carpet either. At the end of the day, if there are different rules in the finals, just let us know."
Earlier in the game, with Melbourne leading 6-0 during the first half, Klein missed a clear knock on from Grant.
Melbourne would march down field and score in the next set, with Klein having little no excuse for missing the decision given his positioning.
Roosters coach Trent Robinson said it was a clear knock on.
"It was pretty clear it was dropped. He was right there, it hit the ground, what can you do?" Robinson asked.
"It was an error, and they went down the other end and scored. We should have also stopped that, but it would have been a try-scoring opportunity to us ten metres out from the line and in finals games they are always critical."
Robinson admitted his side should have defended the mistake, and wasn't expecting any 50-50s to go their way.
"Being really clear, we don't expect 50-50s. It's not the way it has gone statistically in the competition," Robinson said.
"That's not a big issue for us. We should have gone down and defended the play at the end of it. They shouldn't have scored from a penalty ten metres off their own line and we should have been better."
On air audio appeared to pick up referee Klein apologising to Roosters' captain James Tedesco, and while the skipper said he couldn't remember that, he said the knock on was very obvious, even from his position 30 metres away.
"He just said he called it as he saw it. I was 30 metres away and could see that he dropped it, but he was right there" Tedesco said.
"It's hard when you can't have a conversation at the back. That's how he saw it, but I think it was pretty obvious."
Melbourne coach Craig Bellamy agreed that it was a knock on, but suggested not all the blame should be placed on Klein for the error.
"I didn't have a look at the replay, but I thought live it looked like a knock on," Bellamy said.
"As I said, I thought Harry did drop that ball and it was a big call, but it is hard to blame the referee for everything. He has touch judges and a guy in the bunker. At the end of the day, I can't really control any of that and I don't really want to."
Klein appears to be in a direct battle with Adam Gee to referee the grand final.
He has been rated as the best referee in the game for a number of years now, refereeing in all three games of this year's State of Origin series, as well as the 2022 Rugby League World Cup. He has refereed Origin for a number of seasons and officiated last year's grand final between the Penrith Panthers and Parramatta Eels.
Regardless of whether he is appointed to referee the grand final, Klein will likely hold onto his spot for a preliminary final next week, with the first to feature the Panthers against the Storm at Homebush on Friday, and the second to be between the Brisbane Broncos and winner of the New Zealand Warriors-Newcastle Knights semi-final in the Queensland capital on Saturday.