Alan Pardew will speak with the West Brom board this week after the Baggies' sixth successive defeat.
Albion got off to a flyer when Salomon Rondon poked home in the 7th minute but were pegged back by Jamie Vardy's excellent volley.
It got worse after the break when the Baggies conceeded three second half goals to remain rooted to the bottom of the Premier League - eight points adrift of safety.
Speaking in his post-match press conference Pardew said: "Before you even ask me the question, will I speak to those upstairs? Yes I will. Of course I will because it's getting difficult.
“My pride on the sidelines is such that I don't want to stand and watch that last 15, 20 minutes.
“My teams are better than that and I want my team here to be better than that.
“So I'm going to make sure – and I told the players afterwards that that was unacceptable, that last period of the game.
“In terms of the team, the results and everything it is what it is and I want the best for West Brom.
“For me, it's about planning for next week and getting ready for a difficult game at Bournemouth and that's what I will do.
“But I will still talk to them and get a feeling of what they think because they might think a change is a better thing for the club, I don't know.
“But the one thing I'm not going to do is what I said on Thursday, is I'm not going to lay down tools.
“I said to the players they have got to fight to the end and I'm criticising them for the last 20 minutes because they weren't fighting.
“They've got to fight to the end. I don't care whatever job or workplace you're in, if you're under pressure and you don't want to fight, don't bother turning up.
“So I will continue to fight because that's always been in me, through more difficult times than this by the way, at other clubs.
“I've been there, I'm an experienced manager, I think I know how to set a team up, I know how to make a team strong and resilient but at the moment, when you look at that last 20 minutes, you couldn't argue that.
“I'm not going to accept that and I don't want that going forwards. That's really all I want to say.
“I will see them when I've had a good night's sleep and a glass of wine.”