The forward had scored three times in his previous two games but United boss Ten Hag made headlines before the match by remarking on Rashford's upturn in form that "when your lifestyle is not right you can't perform in the league we have to perform in".
"You don't get the right levels if you don't have a good and disciplined life away from Carrington," he added about a player who twice missed games last season due to off-field issues.
Speaking to Sky Sports just before the game against Palace, Ten Hag insisted the decision to name Rashford among the substitutes was just to "rotate" his players.
"It feels like something has gone untoward," said Redknapp in reaction to the team news. "I don't know the details. But you don't drop a player that has scored two in midweek and against Southampton.
"I'd be nervous to say he is back but he is showing signs of the Rashford from two years ago.
"It feels like something's happened maybe this week, I don't know the manager's frustration. It is unusual for a manager to out players for their lifestyle.
"Sir Alex Ferguson would have never done it, whereas Ten Hag has done it on a few occasions. It is not always beneficial to the players."
Speaking after the goalless draw, in which Rashford was used as a substitute after 61 minutes, Ten Hag said: "Already there is speculation [about the reason for Rashford's omission from the starting XI]. Pundits.
"As a person you are not OK if you bring such speculation when you don't know [the situation].
"This had nothing to do with [what I said in the pre-match press conference]. I am very happy with Marcus. His defending and his offensive duties. He's scoring at the moment.
"It was just about rotation."
Discussing Rashford after the match, Redknapp said: "I can only imagine when he woke up to those headlines it wasn't enjoyable for him. He was probably going, 'why is the manager bringing that up?'
"Initially I read it and it was almost like, 'we've figured it out and this was why Marcus wasn't doing as well last year, he wasn't living his life the way a professional athlete should'. But obviously it's been taken slightly differently because he gets left out today. I don't know what's happened this week, it might come out, it might not.
"Rotation? He played 63 minutes in midweek and got two goals. You don't take a player that has two goals [out of the team]. Do you think that they're going to do that with Mo Salah at Liverpool? It's just not going to happen.
"Something has gone on that we don't quite know." Ten Hag refutes this.
"But if there is something a little untoward and he's not living his life right that's something only [Rashford] can take control of," continued Redknapp. "You've got to make sure you're on it all the time.
"I liked a night out, we all did. But you have to make sure that you live your life right more so than ever. In my day, pretty much everybody else was doing it. But not now. Every single day you have to dedicate your life to football. He needs to go back to that player of two years ago when he was ripping it up.
"[Last year] it became, at times, hard to watch. There were certain games where he'd trot around and plod and not really look like he cared. Man Utd fans will always want you to make runs and show you care because they'd give anything to have that shirt on. It's only probably one day where he looks back and thinks 'why didn't I give a little bit more at times'.
"He's got God-given talent but we need to see the Rashford of two seasons ago."
