The Dutchman was finally put out of his misery on Monday following United's 2-1 defeat to West Ham, which left the club sitting in 14th place in the table.
Ruben Amiron now looks set to follow Ten Hag into the Red Devils dugout, but Stam believes the club should have given the former boss more time in the job.
Talking to BetMGM, the former defender, who won the treble with United in 1999, feels after being given a new contract in the summer, the board should have stuck with their man.
“If they wanted to remove Erik ten Hag as manager then they should have done it in the summer, " Stam said.
"When you’re looking for other managers and talking to other managers, I don’t think it’s good for the current one.
“If you’re not sure about them the decision needs to be made there – but if you agree to a new deal and still want to go ahead with Erik then you need to follow through and support him in the long term.
“The way it was done at this moment in time was a harsh decision and, for me, done a bit quickly. Only two months or so after signing a new contract seems a bit too early to me and I think he should have been given more time.”
United got back to winning ways on Wednesday with a Carabao Cup victory over Leicester, but it's the league form that has been the biggest concern, while in Europe, they have failed to win in nearly a year.
Stam believes that while the boss should be partly to blame, the whole club needs to take responsibility for its current predicament.
Adding: “The United players clearly need to step up and they haven’t been performing at the level they should have been – but this is a whole club thing.
“The manager should take responsibility as he’s responsible for the team but higher up things need to be better too; the recruitment and getting the right players in for the correct system and style of player has been lacking.
“If you want to win trophies and challenge the best sides, you need to be consistent and these players haven’t been.
“They are playing for one of the biggest clubs in the world and need to show it each and every week and challenge their team-mates to be better – but we haven’t seen that happen very much in recent years.”