Jonny Bairstow's controversial dismissal was not in keeping with the spirit of the game, Sunak's spokesman told reporters.
"The prime minister agrees with (England captain) Ben Stokes who said he simply wouldn't want to win a game in the manner that Australia did," the spokesman said.
But Sunak, a keen cricket fan who watched with Prince William from the Lord's pavilion on Saturday, also deplored the Long Room abuse directed at the Australians by Marylebone Cricket Club members.
"He thinks it was right that the MCC have taken swift action to suspend any members accused of poor behaviour," the spokesman said.
Sunak believed that the standing ovation given by MCC members to Australia's hobbling spinner Nathan Lyon, as he came out to bat on Saturday, was "much more in keeping with the spirit of the game".
But Sunak has no intention of lodging an official protest with Australian Prime Minister Anthony Albanese, to reprise the serious diplomatic strains created by England's 'Bodyline' tactics in the 1932/33 Ashes Down Under.
While there is a "friendly rivalry" over sport between the two leaders, Sunak does not view cricket as a core diplomatic issue, the spokesman remarked.
"The game did provide an opportunity to see Ben Stokes at his best and it was an incredible Test match - he has confidence that England will bounce back at Headingley," he added after Stokes hit a blazing 155 in the second Test.
