The Professional Game Match Officials Limited released a statement on Saturday evening after Marriner dismissed Gibbs for a hand-ball committed by Alex Oxlade-Chamberlain which resulted in a penalty in the 17th minute of the match.
"Andre is an experienced referee and is obviously disappointed that an error of mistaken identity was made in this case," the statement read.
"Incidents of mistaken identity are very rare and are often the result of a number of different technical factors.
"Whilst this was a difficult decision Andre is disappointed that he failed to identify the correct player.
"He expressed his disappointment to Arsenal when he was made aware of the issue."
The Football Association earlier confirmed that Arsenal will be able to appeal the red card.
"Clubs can appeal mistaken identity to The FA, although The FA can pro-actively review also," an FA tweet read.
"Following a red card clubs can also review possibility of a wrongful dismissal claim to The FA, unless dismissal is for 2 yellow cards."
There is a precedent for the decision to be changed after League 1 side Preston had the wrong man sent off against Port Vale in November.
Striker Joe Garner was suspended retrospectively for three games after midfielder Neil Kilkenny had mistakenly been sent off.
Gibbs' mistaken red card would not have happened under UEFA's extra-officials policy, according to a spokesman for president Michel Platini.
It is a situation that Pedro Pinto, the chief of press for Platini, said could have been avoided if there was an extra assistant on the by-line.
Pinto wrote on Twitter: "What confusion at Chelsea-Arsenal with the pen decision. That's why over 30 European countries have endorsed UEFA-backed 5 officials system.
"With an additional assistant referee on the end line, referee would not have got that sending off wrong. Technology is not the answer..."
Pinto claimed that "more eyeballs" were the key to improving referee decision-making rather than technology alone.
The Premier League has employed goal-line technology for the first time this season but it would not have aided Marriner's decision at Chelsea because it only determines whether or not a shot has crossed the line.
Pinto added on Twitter: "More eyeballs are the answer. GLT helps with goal line decisions, but five officials system gives referee more angles of vision. It's not one vs the other."