Sebastien Haller’s 56th minute strike for the Hammers at Brammal Lane condemned Sheffield United to their eighth league defeat of the season and leave them bottom of the table just a point to show for their efforts.
The Blades were the surprise package in the top flight last season, finishing ninth after gaining promotion from the Championship but have struggled to replicate that form this time round.
"It's great how you guys talk about people's careers so flippantly, I love all that,” Wilder said when asked if he feared for his job.
"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."
Wilder has been at the club since 2016 and has overseen two promotions with a side he also represented as a player.
"We were in League One when I arrived and now we are in the Premier League," the 53-year-old Englishman added.
"It's a ruthless, relentless division and a cut-throat division which doesn't give you handouts.
"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."
