Martin took the Saints job after they were relegated from the top flight in 2023 and did not have the ideal start when they lost four games in a row early in the Championship season.
However, Southampton turned things around to finish in the play-off spots before beating Leeds United in the second-tier play-off final at Wembley in May to win promotion.
"It's the job, I don't enjoy it, it's not a problem. It doesn't overwhelm me one bit," Martin told reporters on Thursday.
"It's the same last season, we had a period at the start where we had a really tough time and then people can say what they want with very little recourse and will judge us based on a highlights reel of eight minutes so I treat it all the same.
"Because those same people who said things after losing four games last season spoke about what a brilliant job I did at the end of the season.
"There were people that called me a terrible appointment for the club and said they needed to make a change after losing four games. There will be the same people doing that now after three games, three defeats, so I treat it all the same."
Southampton, who are second-bottom with no points after three games, host 14th-placed Manchester United on Saturday.
Martin said his side are still coming to terms with the "level of competition" in the Premier League and added that there would be changes even as he tries to stay loyal to the players who helped the club get promoted.
"After three defeats, there inevitably will be changes. How many - you'll have to wait and see and who. It's such a difficult position because I feel fiercely loyal to players who have got us into the Premier League," he said.
"So I have to balance that loyalty from what they did last season to what some of them are actually doing now and the place they are in right now."
