Morata – on an 18-month loan deal from Premier League side Chelsea – made it three goals in two matches with a pair of headers in the 2-0 La Liga victory at Sociedad.
The 26-year-old, who struggled for form and goals before moving to Atletico in January and opened his account last time out against Villarreal, scored twice within three minutes prior to half-time.
Morata revelled in his match-winning display post-match, telling beIN SPORTS: "Most of the time, forwards are judged by their goals but, above all, I have adapted well and quickly.
"I am very happy because I have had a bad time in the past.
"I have adapted quickly thanks to the help of everybody at the club and my colleagues."
Morata's goals helped Atletico stay within seven points of La Liga leaders Barcelona and head coach Diego Simeone was full of praise for the Spaniard.
"When we sign a player we always envision his best side, some adapt faster than others," Simeone said.
"More than for his goals, I am happy for the work he is putting and for how he has adapted to the team.
"Those who have hierarchy take less time to adapt, he is not a kid and he meets the conditions we set for him."
After Morata scored in the 30th and 33rd minutes, Atletico were reduced to 10 men when midfielder Koke was shown a second yellow card just past the hour-mark in San Sebastian.
Sociedad, however, were unable to make the most of their numerical advantage as second-placed Atletico moved five points clear of city rivals Real Madrid.
"It wasn't an easy win," Simeone added. "I think that Real Sociedad started the match very well and we had difficulties in the first few minutes. We improved our passing after Willian Jose's injury and we finished the first half very well.
"After Koke's red card we had to defend inside our box in order to win a very important match."