The Dutchman had predicted a lonely race in which he would be unable to keep pace with either Mercedes or Ferrari - but in the event, he finished just a few seconds behind Kimi Raikkonen, having shadowed the Finn for the duration of the season-opening Grand Prix.
"I'm still a bit surprised that I was quite close to Kimi," Verstappen said after the race.
"I think the car behaved quite a bit better in the race than in qualifying. It's difficult to say how much [Red Bull still trail Mercedes and Ferrari], but it looked a lot better in the race.
"The race was a lot more positive than qualifying; I'm happy about that.
"We still need to improve, and we will - and we'll see what happens in the next few races."
While Verstappen finished fifth, team mate Daniel Ricciardo suffered a string of misfortunes as a gearbox sensor issue forced him to start from the pit lane two laps into the race, before a separate engine problem prompted his retirement.
"Obviously I'm disappointed today, but I'll wake up tomorrow and prepare for China," Ricciardo said. "It's been a long week.
"Don’t get me wrong it's been fun, I just feel bad for everyone, the fans. I'm sure they would have loved me to get out and race.
"If I look on bright side, the positive was that Max seemed to have relatively good pace - so maybe we can learn from his race pace and as a team move forward."