Pietersen's future came into question following the drawn second Test against South Africa, with the batsman alluding to problems in the dressing room.
Strauss believes that any problems should have been dealt with inside the the dressing room.
"I'm a big believer in not airing dirty laundry in public," said Strauss.
"It's one of our core values in our team that what goes on in the dressing room stays in the dressing room. Any time anyone has fallen foul of that they have been disciplined - and rightly so.
"It's about mutual respect and trust, and that is a core issue that is central to resolving this."
England must win the third Test against South Africa in order to remain at the top of the Test rankings.