"What I find a bit rich [is] everyone's attitude towards, 'You're only in the game for so long and you've got to make the most money possible and set yourself up'," Fittler said, on the Sunday Footy Show.
"I think that's a crock, it's a total crock.
"You've got to build your nest egg and chase all the money you can. How many times, Joey [fellow panellist Andrew Johns], did you decide to stay at Newcastle, because you were happy, your friends were there, you had a good footy team, you love the team and you love the club?
"How many times would you have stayed [in Newcastle when coming off contract]?"
Fittler raised the matter in a segment when Jack Bird's move to Brisbane was being discussed, but didn't specifically mention the 22-year-old. Bird is yet to speak publicly, since news broke of his deal with Brisbane worth a reported $1 million a season, but it's widely assumed his motivation to head north was sparked by a desire to play closer to the ball at five-eighth, rather than staying out wide, where he currently plays at Cronulla.
Tigers captain Woods has spoken often this season about his responsibility to his family being one of the main drivers behind what he decides to do with his next contract. He's spoken passionately about players needing to do what's best for themselves and their loved ones, when it comes to deciding what direction their career will take.
While few would criticise players doing what's best for their families, Fittler is clearly upset at the lack of loyalty in the game these days.
Melbourne fullback Billy Slater said Bird's decision to leave the Sydney Shire, after what will have been nearly three full seasons in first grade at the Sharks, was a reflection of the trend emerging among young players in the NRL.
"It's just the way the game is at the moment," Slater said. "Young players are willing to test the open market and leave clubs.
"I think, back in the day, you stayed the majority of the time where you've come through, but it's just the way the modern game is at the moment.
"You've got to be happy. If you're not happy, it doesn't take long for your footy to fall away if you're not in a happy environment and a successful culture.
"He [Bird] has got that down at the Sharks and the Broncos have certainly got their successful culture too, so he's not going to a different place there, but you've go to be happy."