Adkins was removed from the manager's seat at St Mary's despite a successful 27 months in charge that has witnessed back-to-back promotions.
Under Adkins, the Saints won twice as many games as they lost and rose more than 40 positions in the league.
They currently stand 15th in the Premier League, following a run of just two defeats in their last 12 matches.
Adkins has now been replaced by Argentinian Mauricio Pochettino, with Southampton's executive chairman Nicola Cortese explaining the decision as being made "with the long-term ambitions of the football club in mind."
And Perry McMillan, of the Southampton Independent Supporters Association, is the latest person to criticise the sacking of Adkins.
McMillan wants the club's fans to wave handkerchiefs at St Mary's on Monday when Everton arrive on the south coast for a Premier League match
He told the Daily Echo: "As Spanish supporters wave white hankies as a form of protest it seems an appropriate way to protest at Nicola Cortese's ruthless treatment of Nigel Adkins.
"It's important we send out this message and as this match is live on TV and will be seen throughout Europe, it's a great opportunity to show how we feel.
"When you think about how hard he (Adkins) worked to get us into the Premier League, this leaves a bitter taste."
Southampton v Everton is live on Sky Sports 1 this Monday. For more details click here http://www1.skysports.com/footballonskysports/8395413?DCMP=FootballHub_SouEve_Editorial