Dyson, in his first senior game of the season, had just been subbed into the match when he gathered the ball in defence and took several steps before being caught by Tigers big man Tyrone Vickery.
The Bombers midfielder appeared to get a clean handball away as soon as he was tackled, but was penalised by the umpire for incorrect disposal.
Vickery then kicked a goal from the free kick, giving Richmond a 16-point lead midway through the third quarter.
Gieschen told afl.com.au that the whistle-blower's decision was clearly wrong.
"It's quite clear cut," the umpires boss said on his weekly show, What's Your Decision?
"We can see Dyson get a handball, he got a fist away.
"He had a prior opportunity, but when he gets tackled he can still handball it or kick it immediately, and he did that.
"We can see that he gets a fist to the ball, and it should have been a play-on call.
"So Ricky Dyson, very unlucky there and we apologise to him."
Watch What's Your Decision? for footage and Gieschen's full explanation of the incident, plus the umpires manager's verdict on:
• Holding the ball against Essendon's Tayte Pears
• Incorrect disposal against Port Adelaide's Dom Cassisi
• Key forwards Jay Schulz (Port Adelaide) and Barry Hall (Western Bulldogs) not penalised for 'hands in the back'
• A confusing free kick against Collingwood forward Travis Cloke
• Two 50m penalties against the Western Bulldogs
