Southampton were 5-0 down to Tottenham before half-time and frustration from some of the home fans was directed at both Martin and club owners Sport Republic.
Despite making nine permanent signings in the summer, Saints’ squad has been exposed in the Premier League, with the lack of goals and a porous defence.
“This is a very precarious job,” said Martin after the game. “I can’t sit here after losing 5-0, being bottom of the table and pretend I’m feeling confident about my job.
“I’ve no choice but to work and to fight. That’s all I’ve done in this job and I’ll continue to do that until I am told otherwise.”
No team has ever had five points or fewer at this stage of a Premier League campaign and avoided relegation.
Martin has refused to compromise on his possession-based passing principles but it has not worked as:
Southampton’s next league game will be a trip to Fulham before they host West Ham and travel to Crystal Palace before the end of the year.
“They have imploded a lot,” Sport pundit Danny Murphy told Match of the Day 2.
“Football is ruthless and when you are at the bottom and the hierarchy and supporters want to stay up, you are going to get moved on. Someone else is going to come in and have a hell of a job but I think it’s too late.”
He added: “You have to be more flexible than he [Martin] was. Ultimately, in the Premier League if your recruitment isn’t very good and you don’t have a lot of Premier League experience, you are going to struggle and that is what happened.”
Southampton fans held up a banner at the game against Spurs which read: “RM: Get out of our club!”
“It is harsh seeing the Russell Martin banner. Not long ago he got them up and was a hero,” former Republic of Ireland keeper Shay Given told MOTD2. “The Premier League is a big step up from the Championship.”