Palace were thrashed 5-0 by the Gunners having now won just one of their last 12 games, a run of form that leaves them just five points above the relegation zone.
During Saturday’s match, a series of banners unfurled in the away end slamming the Palace board reading ‘wasted potential. On and off the pitch, weak decisions. Taking us backwards’.
Another on display said ‘No shared vision. No structured plan. Parish out, Yanks out,’ with Palace chairman Steve Parish watching on stony-faced inside the Emirates.
Hodgson, who returned to the club last season to steer Palace away from a relegation battle, has also been criticised with Graham Potter, tipped as a potential replacement for the 76-year-old in attendance on Saturday.
Asked if he can understand the frustration among supporters, Hodgson told TNT Sport: ‘I can, because we are going through a very bad spell.
‘We were hoping this year to really kick on and that has not happened. I think there are reasons for that, it’s not quite as simplistic as all that, but fans are always entitled to their opinions.
‘They care, they want to see a strong Crystal Palace team and at the moment today they have seen a team that has been outplayed by a superior opponent and I think they are entitled to make their opinions felt.
‘But I’m afraid there are times when we look at it from our position and say, what more can we do? We need people we are trying to get on the field to try and get us results and it is not always that easy.
‘As far as I am concerned, the fans are quite entitled to their opinions and I’m pretty certain now they will let the club know.’
Asked if he felt the messages of discontent were also directed at him, Hodgson added: ‘Managers always take responsibility, the full brunt of it.
‘How does it make me feel? It makes me feel a bit sad, it makes me feel a bit disappointed of course because I think we are doing the best job we can possibly do.
‘But I’m a manager of a football club that isn’t in a very good position at the moment so everything that happens to managers in that position will happen to me.’
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