Marcos Alonso's brace cancelled out a Michy Batshuayi own goal as Morata won in his first start since his £68 million move from Real Madrid earlier in the summer.
Spurs had twice as many shots as Chelsea and 67.5 per cent possession against their rivals but the 24-year-old frontman hailed the fight shown by Antonio Conte's side.
"It was a match where I did what the coach asked," Morata said at Wembley Stadium. "Fight and close spaces. We suffered all together but we won the three points"
"Today, I fought with the centre-backs. He [Conte] said that we had to win today, that was the most important, but to take three points here is not easy. Here [in England] you can't stop to rest or think with the ball. The game is all very fast and different."
Morata was impressed by the Spain team-mates who play alongside him at Chelsea, but he reserved special praise for the match-winner, saying the uncapped Alonso should be called up for Julen Lopetegui's next national team selection.
"Hopefully all the [Chelsea players] are possible call-ups," he said when asked about his team-mate's chances. "There are many here who deserve it. First, I have to think for myself, because I don't know if I will be [called up].
"And then all players are possible — especially Marcos [Alonso], who has made a nice game."