Kilmarnock boss Alex Dyer believes he maintains the support of the board after a fifth straight defeat, but will have no problem if the club decides his time is up.
Killie suffered their eighth loss in nine Scottish Premiership matches after Scott Robinson's stoppage-time volley was caught up in storm-force winds and looped over Danny Rogers and under the bar to steal a 2-1 victory for Livingston.
Chris Burke had given the hosts a 48th-minute lead from the spot after Nicky Devlin was penalised for handling on the ground.
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But Jay Emmanuel-Thomas levelled from long range three minutes later and substitute Robinson won it for Livi in the dying seconds.
Dyer said: "It's difficult to take. We were in the game and we would have taken a point given the run we are on.
"It wasn't to be as they've scored with the last kick of the game and it's a sickener for myself and the players."
When asked if he was questioning himself, Dyer said: "I'm a simple guy and I know what I know. I've been around the block a little bit so it's not a problem.
"The boys are hurting. It's obvious the boys want to change things but they need a little bit of luck. But we have to stay together and go through the bad times.
"We've had two good years at this club where we finished fifth and third and we have to regroup. We have to regroup and go again until someone tells you otherwise."
When asked if he thought he had the board's support, Dyer said: "Of course I have. I've got no problem.
"The board are a good board. If they turn around tomorrow and say it's time, I will shake their hands and I will move on, it's not a problem. There will be no animosity, there will be no hatred, because they have always been good to me since I have come here.
"So it's not a problem. I know where I'm from and I know what I've got and I'm lucky enough to be at a good football club with good people. So it's not a problem."
Dyer, whose side face Motherwell at Fir Park on Wednesday, added: "The players are working hard, they are trying their best. We got sucker-punched today and that's life. It's just the way it is.
"We have to dig in, stay together and work hard until someone says you can't work hard any more together."
Livingston are at the opposite end of the spectrum in terms of their form as they recorded their sixth win out of six since David Martindale took charge.
"Today was the first time we'd gone behind since I took over, and it was fascinating for me to watch the boys and see how they reacted to that because they hadn't been in that position," Martindale said.
"But the fact that we bounced back immediately in these terrible conditions just sums up everything about Livingston.
"It was definitely a test of character to go behind to a goal like that. Nicky was saying that his elbow was tucked in but the ball did strike him, although it was hard for it not to be a handball from that distance."