The right-back featured in Diego Simeone's starting line-up as Atletico beat Chivas on penalties after a goalless draw in the International Champions Cup in Texas on Tuesday.
Trippier spent four seasons at Tottenham and helped the club reach the 2018-19 Champions League final before making a reported €22million switch to the Wanda Metropolitano.
Atletico's task against Chivas was made tougher by Marcos Llorente's 24th-minute dismissal, but Trippier was proud of their response.
"I thought we reacted well," said Trippier. "The mentality of the team was unbelievable, we continued to press and try to win the ball back quickly.
"We want to win, no matter who we play. That's the mindset from this team and this coach.
"Two wins from two games, and long may it continue."
He added: "I'm extremely proud to be here and willing to give it my all.
"The supporters have been incredible. They've been so nice to me and welcomed me with open arms.
"I'll do my best for the shirt."
🏴 @trippier2: “I’m extremely proud to be here and willing to give it my all. The supporters have been incredible. I’ll do my best for the shirt.” 👏— Atlético de Madrid (@atletienglish) July 24, 2019
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