Martin was speaking with broadcasters ahead of their Premier League game against Manchester City at the weekend.
The Saints have not won so far in eight league games after promotion from the Championship.
Martin stated: "In this profession, in this industry, you're just allowed to ask about people's jobs all the time.
"I'm here, I have a really good relationship with the owners. We're trying to build and grow something, build on what we've done over the last 16 months.
"I'll continue to do that to the best of my ability with the same love and care I have in. We have the same will and want to improve with the same work ethic.
"Until I'm told otherwise, I will do that. We (the owners) have a really good, honest, open relationship. I want more points, they want more points.
"Should we have had more points? Yes. I think if the performances and the data suggested much differently, then maybe it's different conversations.
"But I feel that nothing but support from them right now. It just it won't impact my job either way," Martin added."I walked into training and on your channel it was breaking news that I'm still in a job. So how that becomes breaking news at any point is incredible."It was because everyone's desperate to see the first manager sacked in the Premier League. Bookmakers, you guys, the TV, because it creates drama.
"Then they can talk about the next manager. I don't listen to it in the same way I didn't listen last season when we were having a good time - but I find it fascinating.
"I find it all fascinating. The circus and the level of drama around the Premier League. There was never a conversation about Leicester being do or die.
"I knew that. Although lots of people reported it to be that way. But as I said, there's never a comeback for that after so people can say why hasn't it happened.
"Now we have one of the toughest challenges we have (against Man City), and that's my focus. It's not about what's gone on previously.
"It's about the people inside the building and the people that gave me the job and gave me a new three-year contract in the summer.
"They know I continue to do my very, very best and we're open to learning. We're trying to adapt and we're trying to grow a team in our way.
"I do think the level of criticism or scrutiny we face compared to a lot of others who probably have different expectations from us is really interesting.
"Really interesting. I've not been surprised by one bit of it. Not one bit of it."