Chris Wilder would only step down as Sheffield United boss if he thought it was the right thing for the club.
The Blades are bottom of the Premier League with one point from 13 games this season, nine points adrift of safety.
Their 12th defeat, 3-2 against Manchester United on Thursday, was an eighth on the bounce.
Last week the club’s owner Prince Abdullah said he would “stick with Chris no matter what”.
At his press conference ahead of Sunday’s trip to Brighton, Wilder was asked about the possibility of a point coming where he would walk away.
And he said: “I’d only do that if I thought it was the right thing for Sheffield United, that’s the only time I would do that.
“The club means far too much for me for it to be about me. It’s about what happens for the club.
“Whether people above me are giving me their support, or the decisions or whatever, I understand and respect that. I’m working away. As seen in last night’s performance there is still plenty of heart and spirit in this group.”
Wilder also reiterated that he appreciates the support he has had from Prince Abdullah, while stressing “my work and approach doesn’t change here.”
And he said: “I talk with the owner and we’re not happy with the results, of course, he isn’t and I’m certainly not.”
After the Brighton game, Wilder’s men host Everton on Boxing Day, travel to Burnley three days later and are then at Crystal Palace on January 2.
Wilder said: “I think we must win a game before Christmas. The gap can’t grow. Four games in quick succession – we have to take a healthy points total if we are going to give ourselves an opportunity of staying in the division.”
Asked if he will be able to enjoy Christmas this year, Wilder said: “No. I don’t think a lot of people will enjoy Christmas this year, with everything that is going on in the world, let alone what’s happening in the football world, and then let alone what’s happening at Sheffield United.
“I’ve got a switch, of course – I’m going to go into the players and be positive with them. Overall it’s going to be a tough Christmas period and hopefully I’m smiling come the end of it.”
Striker Oli McBurnie (shoulder) is a doubt for Sunday, as is midfielder Sander Berge (hamstring), who came off early in Thursday’s contest.
There was a heated-looking exchange of words between Wilder and opposite number Ole Gunnar Solskjaer late in the game, with the latter seemingly unhappy about some of the tackling.
Solskjaer later said he had gone “maybe overboard with a word” and had apologised.
Wilder said of the incident on Friday: “Just words, because we want to win. He said something and obviously got a reply back from me. It was done and dusted straight away.
“I have a huge amount of respect (for him). He understands we’re going to make contact with them. He’s passionate about his club, I’m passionate about mine.
“But no issue at all, shake of a hand afterwards, wished him all the best, had a beer.”