Anderson insists the urbane Cook has a "mean side" too, and is confident he can harness that to winning effect in his and returning coach Peter Moores' much-vaunted new era.
An urgent reaction will be needed, to England's debacle in Durham where they lost to Sri Lanka by 157 runs two days ago, if the predicted rains somehow avoid Manchester today.
If Cook reports fit after the groin injury which ruled him out in the north-east, to take over again from stand-in capain Eoin Morgan, the third Royal London instalment represents a pressing opportunity for him to show his mettle - and for the likes of Anderson to help him do so.
"He is a nice guy - but he's got a mean side to him as well," said Anderson, who concedes he and other established players must make sure they give Cook more support than they managed at times during England's descent to a 2013-14 Ashes whitewash.
As the new Cook-Moores regime seeks to set the tone, the next engagement in a one-day international series tied at 1-1 with three to play will be a telling one.
Anderson added: "I think he's the sort of guy that looks to improve constantly . . . and I think that's something we'll definitely see over the next few months. He's going to be given a lot of responsibility, I think, on and off the field - and I'm sure he'll thrive on that.
"I don't think, over the winter, senior players helped as much as they could with taking pressure off Cooky. A captain's job is difficult, and he needs his senior players around him to share the burden."
Pace linchpin Anderson, who will be 32 in July, has no hesitation in acknowledging he was among those who could have done more for their captain in Australia.
"I think the senior players have got a huge role to play," he said. "As a captain, it can't always be his job to discipline people or think of tactics or make bowling changes. It's everyone's job to be thinking about the game, how the team can improve and be offering that advice - it doesn't always have to come from the captain.
"When we've done well in the past is when we've had five or six guys who can stand up in the dressing-room and give feedback. That shares the burden and takes a bit of pressure off the captain."
Last winter, by Anderson's own admission, that did not happen as England spiralled from one setback to another.
He said: "When you're in Australia and you get on to a bit of a downslope, you can get a little bit insular . . . start worrying about your own game perhaps. This is a real chance for us now. We've got a new coach and some new faces around; we can really start to rebuild this team."
Moores, formerly in charge of Anderson's county Lancashire after his first stint with England ended abruptly and controversially, must forge an effective management axis with Cook. Anderson said of the coach: "He's the kind to just let everyone get on with their jobs, not forcing too much on us at an early stage."