Wednesday dismissed Jones on Sunday following their defeat at Blackpool and Flitcroft departed not long after Barnsley's 3-0 loss to Birmingham at Oakwell on Saturday.
Barnsley have won only two league games this season and slipped to the bottom of the table, while Wednesday have registered just one win in the Sky Bet Championship and sit one place above their South Yorkshire rivals on goal difference.
Ritchie, sacked by Barnsley in 2006, six months after guiding them to promotion from League One, told Press Association Sport: "I would not advocate anyone getting the sack. I know what it's like because it happened to me, but both Barnsley and Sheffield Wednesday had given them time.
"Sometimes you need a change of ideas to change the mindset of the players.
"I'm surprised at the way it's gone for Dave Jones at Sheffield Wednesday because they've got some fantastic players and Dave is a really good manager."
Ritchie believes owners should do more to back their managers, instead of jumping to replace them so quickly.
He added: "The most certain thing if you are a manager is that you know you are going to get the sack.
"Whenever that is is down to your good coaching or good fortune or lack of money.
"But as a manager you have to keep it moving, bring in new players and if you don't get the financial backing what do the powers that be expect to get?
"I don't understand it sometimes. The manager gets told the team hasn't done this and they haven't done that, but what can a new manager do?
"Initially he can get a good reaction, but will it last? That's the big question."
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