Charlton are now four points adrift from safety in League One following a fifth defeat in eight matches.
Addicks owner Thomas Sandgaard was at Tuesday’s game at The Valley after flying in from the US and there were chants from unhappy home fans for Adkins to be sacked.
Adkins was expected to lead a promotion challenge but Charlton have endured a miserable start to the season and are facing up to the real prospect of a relegation battle.
Speaking after the Accrington defeat, Adkins said: “I have got thick skin. I want to be here, that is an important thing. And for me it is how I can keep putting ourselves in a position to learn from mistakes which are happening because you’ve got to.
“But we all know the reality of football. I will put that to one side and keep doing my job to the best of my ability.
“What has happened has happened. You can’t change it. All you can do is come in and work very hard.
“I can understand when things are going against us, it is a challenge. And someone has got to bear the brunt of the frustration.
“But what you do is have belief in yourself and you learn about yourself even more, you learn about the people you are surrounded with – and how they respond to it.”