The Crows were overrun in the last quarter of a pulsating contest at the MCG on Sunday, leaving them clinging to eighth spot on the ladder.
Controversy erupted in the desperate final moments when Dawson was denied a set shot to win the game after high contact from Collingwood's Jamie Elliott.
Crows ruckman Reilly O'Brien had driven the ball inside 50 metres, where it was gathered by Dawson, who was immediately crashed into by Elliott.
The ball fell free and the Magpies cleared the danger to hang on for the win - their third consecutive victory over Adelaide by less than a kick.
A furious Dawson sustained a cut lip in the incident and was shown on the television broadcast approaching an umpire to voice his concerns.
On Monday, Richardson conceded the free kick had been missed by umpires, who "had a restricted view of the contest".
Crows coach Matthew Nicks later wrote it off as "the luck of the game".
"It's a tough game to play, it's a tough game to umpire," Nicks told Fox Footy.
"You know what, that's probably not paid nine times out of 10 during the year.
"We'd like to think maybe we're two points ahead when that happens, but we'll fight on and hopefully we meet that team a lot more times over the next few years."
If awarded the free kick, Dawson would have had a shot after the siren to win the game for Adelaide from about 40 metres directly in front of goal.
"Watching it back, it was obviously a clear free kick, but it's hard in the heat of the game to notice that," O'Brien told Network Ten.
"Daws had a pretty fat lip with a lot of blood coming out post-game, so he certainly got some contact, but you can't really blame it on individual umpiring decisions.
"There's a lot throughout the game that go either way. We had our chances and just weren't able to capitalise late and get ahead."
Dawson famously converted an after-the-siren shot to snatch victory for the Crows against fierce rivals Port Adelaide in round three last year.
