Pietersen struck a defiant 113 at Old Trafford to become England's leading run scorer, which led to Botham stating that a draw is still possible in the match.
"Pietersen played magnificently," Botham told Sky Sports News. "He was controlled and aggressive when required. He went two-and-a-quarter hours without a boundary after a flurry of sixes; he set his stall out to play a big innings.
"Pietersen was always going to take [Nathan Lyon] on and when he did he suddenly gave Michael Clarke a problem. Does he keep the spinner going? If he doesn't, then there's more work for the seamers.
"It was a tough one but Michael Clarke will be frustrated; that said Australia are still in a very good position."
England will start day four 233 runs behind.