Batsman Pietersen was dropped from the team last week following allegations that he had sent text messages to his friends in the South African squad that criticised some of his England teammates and coaches.
However, skipper Strauss has revealed that Pietersen has work to do if he is to regain the trust that he has lost.
"There's a lot more to investigate with all this. In truth if there's a way forward those issues of trust and mutual respect, we need to deal with it behind closed doors," Strauss told reporters. "It's very important to concentrate on my job leading guys out on the field. I wasn't involved with Kevin Pietersen's dispute with the board but once players are involved it is important I get involved.
"The feelings of the dressing room and the way we interact as a group is of vital importance to me and I'm not willing to turn a blind eye to that.
"It is not between me and him particularly. The texts sound like I was involved in it but it is a broader issue on how we interact.
"He is a world-class player and no-one will deny that, when he is playing well and happy in the dressing room he is a great asset but that's not where we are at the moment. The selectors made a brave and correct decision. With the issues we need to resolve, it would have been untenable to have him in the squad."
Pietersen made his England debut during the Ashes series of 2005.