The former Liverpool defender had sparked a major controversy after suggesting that Emery could be tempted by the opportunity to manage Manchester United should Michael Carrick lose his position at Old Trafford.
Carragher's comments, made during an appearance on The Overlap, angered Villa supporters, particularly after he suggested there was a hierarchy in football that placed Manchester United above their club.
The situation escalated when Carragher responded to criticism from Villa supporters by telling them to “shut the f*** up”, before reiterating that Aston Villa would never be Manchester United.
Villa subsequently issued a statement on Friday evening, signed by co-owner and chairman Nassef Sawiris, announcing their intention to pursue legal action.
“Aston Villa will initiate legal action against Jamie Carragher for his unacceptable insults about the Club and its fans.
“Aston Villa will not allow anyone to stop our ascension in English and European football.
“Nassef Sawiris, Chairman.”
The statement represented a significant escalation in the dispute, which had initially centred on Carragher's assessment of Emery and the possibility of the Spaniard moving to Old Trafford.
However, the Sky Sports pundit changed his position on Saturday, issuing a public apology to the club and its supporters.
“I'd like to apologise to Aston Villa, the owners and their fans,” Carragher wrote on social media.
“My language this week was clumsy and wrong. I can assure Villa fans it was tongue in cheek but I can understand it's not come across that way, so apologies.
“Good luck today UTV!”
Carragher's original argument had centred on his belief that Emery, who has enjoyed considerable success in European football, could reasonably consider a move to a club with Manchester United's history and resources.
The Spaniard has established an impressive record at Villa, including leading the club back into the Champions League and overseeing continued progress in domestic and European competition.
Carragher had questioned whether Emery would eventually want another opportunity to compete for the biggest honours in the game, having previously managed Paris Saint-Germain and Arsenal.
“I think Unai Emery is unbelievable with what he does year after year,” Carragher had said, praising the manager's ability to oversee substantial changes to his squad while maintaining competitive standards.
However, his suggestion that Villa could not match Manchester United's standing in football proved particularly unpopular with supporters.
The apology came as Villa prepared for their Premier League fixture against Manchester City, with the club having made clear that it would not accept what it considered unacceptable attacks on its identity and supporters.
Whether Carragher's apology will be sufficient to bring the matter to an end remains unclear, with Villa having publicly announced their intention to take legal action.