Palace became the first club in top-flight history to lose their opening five league games without scoring a single goal after suffering a 1-0 defeat to Southampton on Saturday afternoon.
Hodgson took control of a team that had lost their first four league games of the 2017-18 campaign, and the Eagles will now face Manchester City, Manchester United and Chelsea in their next three fixtures.
Barton has admitted that he 'did not see the appointment coming', claiming that he thought Hodgson "was done in football" after leaving England following a disastrous Euro 2016.
"I didn't see the appointment coming if I'm honest. I thought they showed enough shoots [of improvement] in the Burnley game to give Frank de Boer a chance. The Palace hierarchy obviously decided that wasn't going to be the case," Barton told talkSPORT.
"I'm looking at Roy [Hodgson] as I'm watching the game and he doesn't inspire me. I'm looking at him thinking, what is he going to do? You can understand when Big Sam [Allardyce] or Tony Pulis goes in there, which has happened for Palace in recent years, and they fire the lads up – they get them together – and you can imagine them rattling a few cages.
"Seeing Roy at the end of that England campaign, firstly, he looked like he had a bit of a meltdown in the terms of his persona and the way he projected himself. People don't really remember that press conference. He didn't really understand why he was in the press conference, announcing he'd resigned as England manager, but he'd been sacked.
"This guy was done in football for me. I thought it was over. And to see him come in and take that Palace job, four games in; haven't scored a goal, with the run-up that was coming – I was thinking this is lambs to the slaughter."
Barton is currently serving a 13-month suspension for breaking betting rules between 2006 and 2013. The former Burnley midfielder will be eligible to make a return to football in June 2018.