Southampton trailed Tottenham 5-0 before half-time and the frustration of some of the home fans was directed at both Martin and the club’s owners, Sport Republic.
Despite making nine permanent signings in the summer, the Saints squad has been left exposed in the Premier League, with a lack of goals and a porous defence.
“This is a very precarious job,” Martín said after the game. “I can’t sit here after losing 5-0, being last in the table and pretend that I feel confident in my job.
“I have no choice but to work and fight. That’s all I’ve done in this job and I will continue to do it until I’m told otherwise.”
No team has ever taken five points or less at this stage of a Premier League campaign and avoided relegation.
Martin has refused to budge on his possession-based passing principles, but it hasn’t worked:
Southampton’s next league match will be a trip to Fulham before hosting West Ham and traveling to Crystal Palace before the end of the year.
“They’ve imploded a lot,” BBC sports expert Danny Murphy told Match of the Day 2.
“Football is ruthless and when you’re at the bottom and the hierarchy and the fans want to stay at the top, you’re going to move on. Someone else is going to come along and have an incredible job, but I think it’s too late.”
And he added: “You have to be more flexible than him. [Martin] was. “In the end, in the Premier League, if your recruitment is not very good and you don’t have a lot of experience in the Premier League, you will struggle and that’s what happened.”
Southampton fans held a banner at the game against Spurs that read: “RM: Get out of our club!”
“It’s hard to see the Russell Martin banner. He lifted it not long ago and he was a hero,” former Republic of Ireland goalkeeper Shay Given told MOTD2. “The Premier League is a big step forward from the Championship.”