Chris Wilder defiantly fended off questions about his future as Sheffield United manager following another defeat on Sunday.
The Blades were a revelation last season on their return to the Premier League, finishing ninth in the table, but are finding life much tougher during their second campaign in the top flight.
Wilder's side have only one point from their nine matches after a 1-0 home loss to West Ham and remain rooted to the bottom of the standings.
Sebastien Haller's strike from the edge of the penalty area after 56 minutes inflicted a fourth straight loss and an eighth Premier League defeat this season.
The Blades are without a win in 12 Premier League matches going back to last season but when asked if he feared for his job, Wilder replied: "It's great how you guys talk about peoples careers so flippantly, I love all that.
"I haven't had the sack in 20 years – 911 games if you hadn't noticed – I don't fear it.
"I need to be careful because I don't want to come across as arrogant and look like I think I'm untouchable, but I don't feel it should be asked given the journey that we have been on over the last four years.
"We were in League One when I arrived and now we are in the Premier League. It's a ruthless, relentless division and a cut-throat division which doesn't give you hand outs. It's not a time to go into our shells and I certainly won't as manager of the football club.
"We have to embrace the challenge and everything that goes with the Premier League."
The Hammers, on the other hand, have 14 points from a tricky opening set of fixtures which has already seen them play Arsenal, Wolves, Leicester, Tottenham, Manchester City and Liverpool, and David Moyes' men are in the top 10.
Moyes said: "I am not getting carried away, but there is a real self-belief at the moment, the football is getting better and better.
"I am not looking down, we are certainly looking up. We want to catch the teams higher up the league, that's for sure.
"We want to keep this run going and keep this momentum going and build on it. I would hope we would always be able to say we want to be challenging for the top eight, but I don't want to promise supporters anything at the moment. I want to actually deliver more than is expected."
A rare Premier League goal for Haller gave the Hammers victory. The Ivory Coast striker has scored four goals in cup competitions this season but his effort on Sunday was only his second goal in the Premier League this campaign and fourth in 2020.
Moyes said: "The big thing about centre-forwards is you want them to score the goals than win you games, and he's done that. I've noticed a big change in his confidence, he is upbeat, and there were parts of his game today that were very good.
"He's been smiling and hugging everyone in the dressing room and he deserves it because it was a great goal."