The veteran bowler, who was knighted last October, followed from home as Ben Stokes' men slumped to a 4-1 defeat amid a fall-out over selection, preparations and behaviour.
"We've seen the backlash of losing in Australia quite heavily. I thought they had a great chance of causing an upset or winning, certainly, out in Australia. I still feel like they've got a great chance of winning in England," said Anderson.
The England and Wales Cricket Board decided not to swing the axe, sticking with Stokes as captain, Brendon McCullum as head coach and managing director Rob Key.
Anderson was reluctant to offer an opinion on whether that was the right call, saying: "They've decided that that's the right way to go. We've seen it in the past where people have lost their jobs after Ashes series and maybe knee-jerk reactions."
But on England's current seam attack, Anderson sees reason for optimism, particularly regarding Josh Tongue, although he sounded a note of caution on Jofra Archer.
"I love Josh Tongue," said the 43-year-old. "I think he's a serious bowler. And I'm sure he'll play many, many more Tests. Jofra, I'm not sure, with his injuries and T20 commitments, with his Test career, what the future looks like for that.
"I thought Brydon Carse did a good job in Australia. Gus Atkinson I thought bowled well without much reward.Â
"I think there's plenty of opportunity now for batters to also put their hand up at the start of the season for a place in that first squad."
Anderson's own focus is now on the county game as he prepares for his first full season as red-ball captain of Lancashire -- even while celebrating his 44th birthday in July.
"There are other times when I wake up and I struggle to walk to the toilet in the morning and think maybe I can't get another year out of my body. So it's just a day-by-day thing, see how the season goes," he smiled.
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