Last Saturday, Alli shared a video to his official Snapchat account, which showed him wearing a face mask in an airport departure lounge.
In the clip, which was captioned "Corona whattt [sic], please listen with volume", Alli zoomed the camera towards a man of Asian appearance before turning it on a bottle of antiseptic hand wash.
"This virus gunna have to be quicker than that to catch me," read the second caption.
Alli deleted the video and issued an apology on the Chinese social media platform Weibo.
The coronavirus outbreak in China has impacted thousands, with the nation confirming on Friday the death toll has risen to 1,380.
While the Football Association (FA) could yet punish Alli, Mourinho highlighted the England international's presence of mind to apologise and express regret.
"It was not his intention to offend, he apologised immediately, regretted and recognised it was a young guy mistake, a young generation mistake and he apologised," Mourinho said.
"So, my conversation [with Alli] was easy, as it was not one of a contradiction of ideas. It was not him not understanding why I was unhappy, so it was so simple.
"What can I say? He regrets and, for me, that's the best feeling he can show, and to have the humility to apologise I think is also remarkable, because sometimes these young people make mistakes and don't realise, so this conversation was so easy.
"I have a son and daughter basically at the same age as Dele and many of my players — I know what social media is for this generation.
"But when you are a public person like footballers are, they have to know and have to be very careful.
"I repeat, Dele is a great guy. The last thing Dele is is anything connected with racism or disrespect, not at all, but these are current mistakes that some people sometimes make. But again, the good thing for me is regret and apologise, so for me it's end of story.
"I'm not the FA, I'm just his manager, his friend. I repeat, at the same age I have two great kids in my house, and I have to act as an educator and I think the best way to do it is immediately his reaction — regret and apologise."