Atletico won 3-2 at Anfield in extra time to reach the quarterfinals 4-2 on aggregate.
Trippier said, "We knew it was going to be very difficult but we needed to stay defensively strong and try and frustrate Liverpool as much as we could. We knew that we'd get our chances if we beat the press of Firmino, Salah and Mane.
"Liverpool are very strong at home, I've played them so many times in the Premier League (to know that) but we knew we'd get our chances and it was about being clinical in those moments and we were.
"The way we play is the way we train. He's [Diego Simeone] like this on the touchline in training, it's a joy to learn from him every day and work with him. I knew I needed a change and when a club like Atletico Madrid come in for you, you can't say no. I'm learning new things every day.
"You've seen how defensively strong Atletico have been over the years and we were again tonight. The substitutes that came on made a big impact for us.
"There are some fantastic teams in the competition. We will focus on ourselves and who knows what will happen at the end of the season."