American Gatlin, who has served two doping bans, was booed before and after Saturday’s World Championship final at London Stadium, and when he was presented with his medal.
“He served his ban and he worked his heart out doing what he could,” said Willie Gatlin.
“He worked to come back, and he worked his way back to championship form.”
Gatlin, 35, clocked 9.92 seconds as he beat second-placed compatriot Christian Coleman and legendary Jamaican Usain Bolt, who was third.
Bolt, 30, was unable to secure a 20th global gold in his final individual 100m race before retiring.
Lord Coe, president of the International Association of Athletics Federation, told BBC Radio 5 live’s Sportsweek Gatlin’s victory was “not the perfect script”.
He added: “I’m not eulogistic that someone who has served two bans has walked off with one of our glittering prizes.”
Willie Gatlin said he was not “upset” by his son being booed because “I know what kind of son I raised, what kind of character he has”.
He added: “The fans booing is disrespectful to the sport. The sport has always been here and is going to be here after he leaves.
“He created a memory that is going to be in people’s minds a long time.”