Cook was given the boot by the selectors on Saturday as they picked the 15-man squad for the World Cup, with Eoin Morgan taking the reins as 50-over skipper.
The opener had made just one ODI half-century in his last 22 attempts, and had led his country to five successive series defeats.
A personal return of 119 runs in six innings on the recent tour of Sri Lanka proved the final straw, with the left-hander appearing crease-bound, tentative and out of step with the modern 50-over game.
And England paceman Anderson, while applauding the effort and attitude of the man who retains the Test captaincy, admitted that, on form, the right decision had been made.
“I think if you’re going on form alone, his form in the last 12 to 18 months hasn’t been near the standard that it needs to be to stay in the team and he’ll openly admit that,” he told BBC Radio Five Live.
“I think I saw an interview with him after the one-day series in Sri Lanka and he said that if he gets dropped he’d have to hold his hands up and say his form hasn’t been good enough so I think there is that.
“I feel sorry for him because he’s done such a lot of work behind the scenes, he’s really taken the captaincy with both hands and he wants to drive the team forward and he’s got a real vision of where he wants the team to go.
“I think that’s probably the biggest disappointment for him, that he won’t be able to carry that on throughout the one-day series and the World Cup.”
England lost the series against Sri Lanka 5-2 and were largely outclassed by the team that has finished runners-up in the past two World Cups.
But Anderson does not lay the blame for that at Cook’s door, citing long-standing issues that England have had playing 50-over cricket.
“It’s not just the last 10 years, I think since the ’92 World Cup final that we got to, I think we’ve been pretty average in one-day cricket,” he added.
“I think we’ve had little flashes of good form, we’ve got to a couple of Champions Trophy finals in that period of time, we’ve become number one in the world for a brief period of time but we’ve never found a formula that works for us to be successful over a long period of time.
“That’s something that we’re all desperately searching for. We’re watching a lot of cricket, we’re trying to learn from guys like (Kumar) Sangakkara and (Mahela) Jayawardene who are some of the best players, not just at the moment in the world, but that have ever played one-day cricket.
“Going to Sri Lanka will be great for the young lads to try and learn from guys like that.”