Olympiakos owner Evangelos Marinakis is believed to have entered the referee's room at the interval of Burnley's Europa League play-off loss at the Karaiskakis Stadium to blast the performance of the officials during the first half.
The home side's bench spilled out on to the pitch in Athens before the break when Slovenian referee Slavko Vincic turned down a second penalty appeal, having awarded the Clarets a spot kick earlier in the half.
It was then reported that more than a dozen representatives of the Greek Super League side ambushed Vincic and his assistants in the tunnel with director of team operations Dourekas Kyriakos reportedly chasing after the officials.
Marinakis, who also owns Nottingham Forest, is understood to have accessed the room, opposite to the home side's changing facilities, where a loud exchange could be heard.
The incident was excluded from reports submitted by the referee and UEFA delegates meaning that it is highly unlikely that it will be investigated by the governing body.
When addressing the media in his post match press conference, Dyche said: “After the incident where they tried for a penalty, which wasn’t a penalty, I don’t know how many people ran on the pitch and surrounded the referee and the linesman and the officials.
"All I keep getting told is respect the officials with your conduct around the referee.
"The scenes I saw at half-time from all and sundry around the referee on their side. They were waiting for the referee. You all saw the feel of the game was different in the second half. You’re left scratching your head.
“There were plenty of people involved in the tunnel, waiting for the referee to come in and let him know ion no uncertain times what they felt."
He added: “We are given very strict guidelines from UEFA and the Premier League about respect towards the referees and we did what we always do in that we walked straight down the tunnel into our dressing room. And at the end by the way too. You didn’t see me speak to the officials at all.
“It was interesting because there were that many people involved. It wasn’t just the people on the bench, it was all sorts of people from the offices. The tea lady was there at one point! That’s a joke.
“But there were plenty of people there making it clear they were not happy with the referee’s performance.”
In a separate incident, three Burnley players who were not in the matchday squad - Ben Mee, Adam Legzdins and teenager Dwight McNeil, who were sat behind the dugouts - had to be relocated after they were spat at by Olympiakos supporters.
The incident happened five minutes before the break and the trio watched the rest of the game in a VIP box with other Clarets staff.
Olympiakos go in to the second leg, to be played at Turf Moor on Thursday, with a 3-1 lead.