Carragher has a long history of winding up Gary Neville on the site, and the Reds icon turned his mischievous ways towards his brother Phil during Tottenham's clash with Chelsea on Wednesday.
The legendary former Reds centre-back made reference to Neville's time as a United coach under Moyes during the Scot's nine-month stint as Red Devils manager in the 2013-14 campaign.
Neville tweeted his admiration for Spurs boss Mauricio Pochettino, which was enough for Carragher to go on the offensive, as he light-heartedly had a dig about Jose Mourinho's career at Old Trafford and Neville's doomed stint as a coach.
Here's how the exchange played out.
Carragher, and Phil's brother Gary, have previous for online games of verbal jousting, and the former Liverpool star aimed a dig at Phil about Jose Mourinho's refusal to purchase a house in Manchester back in October.
Carragher was at it again after Moussa Sow's stunning overhead for Fenerbahce against United in the Europa League back in November.
However, it is not all one way traffic, and United icon Neville landed one on his Monday Night Football colleague in October.