Scarlets head coach Wayne Pivac and Ospreys backs coach Gruff Rees both had issues with how Saturday's Pro12 Welsh derby was officiated.
The first half of the game lasted almost 15 minutes longer due to video replays, while the coaches questioned some of the decisions reached.
Italian Marius Mitrea was the match referee, with Welshman Derek Bevan the television match official.
"These are massive games and... I would like to see top referees," Pivac said.
"When I say top referees I mean Nigel Owens or someone like that in the middle.
"But I don't make those decisions and they'll have their reasons for doing what they do."
Rees also felt that the decision-making between the officials could have been improved, despite his Ospreys side edging a hard-fought encounter 17-15 at the Liberty Stadium.
"[I'm] just incredibly frustrated that we have these communication issues around a full professional league, which encompasses all the countries it does," Rees said.
"I don't think it's acceptable as such. Regardless of them being right or wrong, the process is just so long-winded and irregular. It just dumbs the game down for me.
"Communication issues are out there. We've seen that before round some of these games and the question asked and how it's interpreted.
"You don't get the clarity around that, as well as the technical issues [which] shouldn't be happening in this day and age."
Pivac said he was happy for match officials to take their time in their deliberations on big decisions - as long as the decisions reached were correct.
The Scarlets boss felt there was an issue with Ospreys' second try, which saw the home pack drive a maul over the line.
Ospreys prop Dmitri Arhip was originally credited with the score after 33 minutes, with the try being awarded to flanker Dan Lydiate after half-time.
"I don't think the time they take is the issue, I think it's just making sure you get it right," Pivac added.
"Clearly they had a very good drive and went over the line. We watched it in slo-mo several times and couldn't see the person with the ball, identify who'd scored a try if the try had been scored but somebody saw it clearly.
"I thought we'd done enough to win that game.
"[I'm] pretty frustrated with a few decisions towards the end of the game, which I thought may have given us one more opportunity for a shot at goal.
"The breakdown was the biggest area for me."
The two teams meet again on 3 January in the return fixture at Parc y Scarlets, and Pivac is confident that his side can make the most of home advantage.
"It's very much game on, so playing at home I'd like to think we'll be right in there obviously pushing harder than we were today," he said.
"Certainly there's a lot of frustration in the changing room after that second half and we'd like to think we'll be up for the game next week and hopefully go one step further."