The former Australia spinner suggested Pietersen, who was dropped after being accused of sending derogatory text messages about Strauss, and the England captain should do whatever it takes to sort out their differences - even if that means having a punch-up.
Warne said: "It shouldn't have got to this. Pietersen and Strauss could have gone down to the pub and had a beer and feed, and if they had to punch the absolute whatever out of each other, then so be it."
He added: "If you have to get it out of your system then do it. Then come back and put your arm around each other and walk out and play together."
Pietersen's management have reportedly issued an apology to the England and Wales Cricket Board, but the player is yet to meet with either Strauss or team director Andy Flower in person and the captain is set to take a family holiday before any discussions can take place.
The row could not have come at a worse time for England, who lost their number one spot in the world Test rankings to South Africa after their 51-run loss in the third Test completed a 2-0 series defeat.
Warne, a friend and one-time house-mate of Pietersen during their time together at Hampshire, said the England team needed to accept the 32-year-old's personality and do more to accommodate it on and off the field.
"From a leadership point of view, I think England have let him down. You have to also understand that some players are a little bit different and need different things," said Warne.
Warne believes the England team's strict approach had conflicted with Pietersen's character. "There are faults on both sides," he insisted. "I think there is a bit too much ego at the ECB. There is no give and take or compromise.
"But I think Kevin will be the first to admit that he has acted in a way that has been a bit silly and stupid and I am sure he would like to take back those actions."