The Palace manager was full of praise for Mitchell - the Academy graduate he brought into the first-team - after the 21-year-old earned his first professional goal and assist in the Eagles' 3-2 victory over Aston Villa.
Hodgson said: "It [the goal] was a fitting end to a very good performance for him throughout the game. It was an excellent cross for Christian Benteke’s equaliser and I thought he worked hard to defend in quite difficult circumstances at times in the first-half.
"In the second-half he continued to work and combined extremely well with Wilf [Zaha] and [Eberechi] Eze down that left-hand side.
"He created chances at regular intervals in the second-half and was often a part of the attack and of course at the end he pops up and scores the winner. It was a great game, very much appreciated by his teammates who gave him a rousing round of applause when he came in after the game.
"His future is very bright and I’m hoping to see him go on to have a very good Premier League career."
Having mentioned the support Mitchell's senior teammates showed, Hodgson was then asked about the defender's popularity, to which he provided a behind the scenes insight.
"He’s popular basically for the right reasons: he works hard, trains hard, always does his job, listens to what he’s being told and does what’s asked of him. He ever shirks any aspects of the game: getting forward to support, running back, blocking crosses to defend.
"That’s what we want from our players and from our left-back. If you do it and do it as well as he does, you’re going to be a popular figure. He shows the players around him, his teammates: ‘Trust me, because with me in your team you’re going to win.’"