"For us it was never a question really, it was all speculation with the captaincy," Anderson, speaking at the Professional Cricketers' Association awards ceremony in London, said.
ALSO SEE I won't quit as England's ODI captain, says Alastair Cook
"From the players' point of view we never thought anyone else was going to lead us to that World Cup, we never doubted.
"For him I think he's had more low points than most this summer, the amount of chat that was going on about his captaincy in the Test matches then the one-dayers.
"So to show the character he has to come through those, it speaks a lot about the guy.
"It was a huge test of character: it's a credit to himself the way he's handled it all.
"I'm sure he had a lot of doubts in his mind of whether he should have captained the Test team or the one day team. But all I can say is from a player's point of view there was never any doubt over who should be captain."
ALSO SEE I won't quit as England's ODI captain, says Alastair Cook
"From the players' point of view we never thought anyone else was going to lead us to that World Cup, we never doubted.
"For him I think he's had more low points than most this summer, the amount of chat that was going on about his captaincy in the Test matches then the one-dayers.
"So to show the character he has to come through those, it speaks a lot about the guy.
"It was a huge test of character: it's a credit to himself the way he's handled it all.
"I'm sure he had a lot of doubts in his mind of whether he should have captained the Test team or the one day team. But all I can say is from a player's point of view there was never any doubt over who should be captain."