The 2010 World Cup champions dispatched Andriy Shevchenko’s men 4-0 on Sunday in the UEFA Nations League at the Alfredo di Stefano Stadium in Madrid.
Fati, who made his debut for Spain in the 1-1 draw with Germany last Thursday, won a penalty from which Sergio Ramos opened the scores against the Ukrainians and scored his first goal for his country later in the first half to give the hosts a 3-0 lead going into half time.
The youngster’s goal made him Spain’s youngest ever goal scorer in history at the age of 17 years and 311 days but Enrique is adamant Fati will not get swollen-headed by his latest feat.
"I'm not scared. I'm sure it won't go to his head, he's very humble," he told a news conference about Fati's first Spain start.
"We're going to know how to manage it. Although I know him, of course he surprised me, that he did that in minute two [won the penalty].
"Sure, he will have bad games, but that self-confidence is not normal to see. Ansu Fati is very happy and has reasons. He is only 17 years old and has to mature, but in his second match with the national team he dares to do all this.
"He brings work and humility. At his age it is easy for it to go to your head, but he is mature enough to know that the path he is following is the best. He is very calm and humble."
Spain climbed to the top of the Group on four points with the win.
