Ponting has backed Warner to be one of the three batsmen for Australia's series against Pakistan.
Pakistan once again produced some sloppy fielding in a 41-run group stage defeat by champions Australia at Taunton.
Warner hit 107 in Australia's 41-run win over Pakistan in Wednesday's ICC World Cup 2019 match at Taunton.
Having lost against India in their previous game, Australia returned to winning ways.
The Pakistani skipper also said that if the conditions are overcast, any team will want to bowl first in Taunton.
Earlier, during the India-Australia game, Virat Kohli gestured in an effort to quiet the crowd who were booing Smith and later apologised to the Australian cricketer.
Pakistan survived a defeat against India in their opening game of the 2017 Champions Trophy before crushing their arch rivals in the final.
Having lost against India in their previous game, Australia will be keen to return to winning ways as they take on Pakistan.
Pakistan can take some heart from that fact that they swept Pakistan 5-0 two months ago in the UAE.
Imam said the confidence he had gained from facing England quicks Jofra Archer and Mark Wood would help him tame the Australia attack.