Writing in Sydney's Daily Telegraph today, he said Warner's actions were an unwelcome distraction at the beginning of a four-and-a-half month tour of England and he must work hard to win back the trust of his teammates and Australian fans.
The explosive opener was fined Aus$11,500 ($11,000) and suspended until the start of the Ashes series by Cricket Australia last Thursday for the incident during the ongoing Champions Trophy.
But Clarke said it would be difficult for opener Warner to keep his place, given what has happened.
"David has been punished and must now suffer the consequences," he wrote in his newspaper column.
"He will miss most of the Champions Trophy and our two lead-up games before the first Test at Trent Bridge, making it difficult for him to retain his place in the Test side.