Pietersen sent texts to members of the South African team during the second Test at Headingley earlier this summer which reportedly contained derogatory remarks about Strauss.
While Anderson felt the Pietersen affair was far from ideal, he added: "He (Strauss) was thinking about this before that stuff started, so I don't think that has been an issue at all."
Strauss, 35, blamed his faltering batting form for his decision to bow out on exactly 100 Test caps last Wednesday, and at the time dismissed speculation that doubts over Pietersen's future had played a part in his exit.
Writing in the Mail on Sunday, Anderson echoed the view of his former skipper. "That sort of thing just wouldn't influence a man like Strauss.
"It was a measure of the man that his reasons for giving up the job were all about what he felt was best for the side."
Anderson praised Strauss for the dignified manner of his exit - which included penning personal letters to his international colleagues.
"What a way to go - leaving all of us a personal, hand-written letter," he said. "Each one was different and the full contents of mine will stay between him and me, but the gist of it was that he was proud of us and that he had many great memories to take with him. Class."
Anderson added that Strauss' leadership style commanded "100% loyalty" from his players.
"Strauss is a great communicator," he said. "Strauss just had a way of reading situations and people and doing and saying the right things at the right time that demanded 100% loyalty."