The Eagles lost 2-1 to Liverpool at Selhurst Park on Saturday, extending their winless run to five matches.
While Hodgson is not at risk of losing his job yet, he has guided injury-ravaged Palace to just one win from their last nine matches ahead of a tough run of fixtures against Manchester City, Brighton and Chelsea over the Christmas period.
With one goalkeeper, Dean Henderson, already out injured, Sam Johnstone left the field in the 87th minute on Saturday due to a calf problem. That saw Matthews come on for his Premier League debut at the age of 29 for the final few minutes, during which time he conceded Liverpool’s winning goal to Harvey Elliott in stoppage time.
“A much better performance”, said Matthews of the game. “We knew what we had to do, from first minute to last we were excellent.
“It shows that everyone is with the manager. The manager has been brilliant. This is the first season I've been with him — I was on loan [at St Johnstone] last year. He has been excellent, and nobody will say anything different.”
Speaking about his Palace and Premier League debut, he said: “No one wants to see anyone come off injured. Sam is one of my good mates so it's never nice, but that is what I am here to do. I've made my Premier League debut and delighted on that side of things, but disappointed with the result.
“I'm 29 now. I've been in the game long enough, waited for my chance and worked hard enough on the training pitch. I got an opportunity, and we'll see what happens next Saturday [when Palace visit Manchester City].”
“We’ll see. I don't want to wish anything [bad] on Sam. I hope he recovers well, and we'll see what happens on Saturday.”
Meanwhile, Hodgson was left fuming at referee Andy Madley's decision to show Jordan Ayew a second yellow card — a decision which changed the course of the match as Mohamed Salah equalised for Liverpool a minute later.
“He’d been on four yellow cards for four matches”, Hodgson noted. “He’s shown such discipline, such determination not to get an extra yellow card. And yet today he’s been sent off with two yellow cards.
“I don’t speak to the Premier League, I don’t speak to referees, I don’t speak to Howard Webb. I just get on with and try and do the best job I can do. That’s all I do.”