Jim McIntyre took responsibility for Dundee's relegation following a 10th consecutive defeat but remained "absolutely determined" to lead them back into the top flight.
Dundee delivered a flat display in a 1-0 home loss against Hamilton with Tony Andreu's 83rd-minute penalty consigning them to the drop with two games of the Ladbrokes Premiership season remaining.
McIntyre had to endure chants of "you're getting sacked in the morning" and "10 in a row, he has to go" during the latter stages of the Dens Park encounter.
The former Ross County boss took over from Neil McCann in October after Dundee lost seven of their opening eight league games, but there has been no lasting improvement.
McIntyre brought in 11 players in January, eight on loan, but an initial three-game unbeaten run has been followed by a club record-equalling run of defeats.
The former Dundee United striker stated earlier this week he expected to be in charge next season regardless of the outcome of their relegation battle.
But he has a major fight on his hands to win over the Dundee support if majority shareholder Tim Keyes and managing director John Nelms do not make a change.
When asked about the fans venting their anger, McIntyre said: "Rightly so. I totally understand it. They have just watched their team get relegated and we have not offered enough to win the game.
"I don't know any support that would be clapping us off the park. It's not been good enough and me being at the helm, I take full responsibility.
"They are obviously hurting big time and so are we. It's hurt like this that we have got to try and use to bounce back up at the first time of asking.
"I'm absolutely determined to do that. It's my responsibility and it's my responsibility to get the club back up. Unless I'm told otherwise, that's exactly what I will be planning."
McIntyre admitted nobody could escape blame.
"We have only scored 28 goals, we have conceded way too many (75)," he said.
"At this level you have got to score at least 40-plus goals and be roughly about minus 20 if you want to have a chance of staying in the league. It boils down to basic maths at times.
"And we have not shown enough consistency. I felt I had to change it in the January window and I still stand by that, because I felt there wasn't enough in the dressing room to get us out of the situation.
"The ones I brought in haven't done the job. I've not done the job. It was my choice but it had to be done, and we have just not had the consistency levels to get a bit of momentum."
Accies created the better chances in the game as they moved four points ahead of St Mirren, who levelled deep into stoppage-time at Motherwell, in the race to avoid a relegation play-off.
Brian Rice, whose team play St Mirren next, said: "It's in our hands now, it wasn't always the case but it is in our hands now.
"But St Mirren are fighting for their life. They got another last-minute goal so they are fighting for Oran (Kearney) but you could see here that our lads are battling their corner."
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