Smith had to leave the green turf at Lord's on Saturday after he was struck on the neck by a lethal bouncer from England pacer Jofra Archer, which knocked him to the ground.
Smith returned to the crease 40 minutes later, before being dismissed for 92. While many fans offered him a standing ovation, an audible contingent booed at and jeered Smith both times, when he was withdrawn and when he returned.
"A draw for the second Test but it was a total Ashes foul for the crowd at Lords to boo Steve Smith," Morrison posted on Facebook.
"His performance on the pitch during his return to Test Match cricket in the UK demands nothing other than respect," he added.
The Australian PM further termed Smith "a champion" and said he is expecting the 30-year-old to answer his "hecklers" with bat and ball in hand to bring home the Ashes.
"He's a champion and has handled the events of the past year with a real humility. I'm extremely proud of Steve Smith, and it's not just because he comes from the Shire.
"The crowd could learn a thing or two from Steve Smith and I look forward to him answering his hecklers with bat and ball in hand to bring home the Ashes," said Morrison. Earlier, former Australian cricketers also condemned the behaviour of the Lord's crowd.