"They might not be around for much longer and it will be easier with the next guys."
While some fans understood Cook's position, others tweeted that it was a sad day for commentary.
"He's basically acting in a PR capacity for his mates," wrote one disgruntled cricket follower.
Cook is particularly close to Anderson, who he has described as England's best-ever cricketer.
When Cook retired following the series victory over India last year, Anderson described him as "an amazing guy".
"He really cares about people, cares about English cricket," said Anderson, who has taken more test wickets than any other fast bowler.