Asked where he needs to improve to get closer to Verstappen, Perez said: "I think today it was really the start that put me out of contention for the race, but it was all about minimising the damage.
"Finishing second was the maximum I could do today.
"It's a long season. I think I'm getting closer every single session.
"I'm feeling comfortable with the car and we have a strong package and I will give my best."
'A dream start'
The Bahrain Grand Prix saw Red Bull secure its first one-two result at an F1 season-opener in the team's history.
Reflecting on the overall result, Perez added: "It's a dream start.
"When we look back at last year and how we started here (a double retirement), it's really nice. It's a nice comeback as a team.
"We worked really hard over the winter so it's great to see all of the boys enjoying the first race.
"We have a strong package so it was important to get both cars to the end."