The Red Bull driver went into qualifying having topped both FP2 and FP3 and, despite also going fastest in Q2, he lost out to Charles Leclerc in the pole position shootout by 0.123 seconds.
The defending F1 world champion conceded his Red Bull car balance wasn't perfect in Q3 but hinted it could have been down to his team focusing on a stronger set-up for the race compared to qualifying.
Verstappen was also heard over team radio unhappy about being told to do a slower preparation lap in his first Q3 run.
"I think it was a bit hit and miss, Q2 seemed quite good and Q3 was a bit of a struggle to get the balance together but nevertheless I think it was alright," Verstappen said.
"We have a good car as well and, at the end of the day, that is the most important and it's a good day. It's a good start to be here.
"Not fantastic but also not too bad, otherwise you cannot be in this position, so there are a few things to look into and try to extract to be better for next time.
"You want to be perfect in qualifying but you also want to make sure your car is working for the race because the points are scored there.
"It was nice, having a good battle with Carlos and Charles at the end, who both did a good job over the winter so I hope it will be an exciting race."
Both Red Bull and Ferrari translated encouraging pre-season and practice pace into locking out the top four spots, with Leclerc and Verstappen on the front row ahead of Carlos Sainz Jr taking third place for Ferrari from Verstappen's team-mate Sergio Perez in fourth.
It meant Lewis Hamilton led the Mercedes effort in fifth, over six tenths of a second off Leclerc's pole lap time, as his team-mate George Russell struggled in Q3 by locking up at Turn 1 on his final lap, causing him to drop to ninth place.
Verstappen suspected Mercedes' claims of it being off the frontrunning pace were false after pre-season testing but, having seen the reigning F1 world constructors' champion struggle during Bahrain GP qualifying, he gave a sarcastic "very, very" in reaction to being asked if he was disappointed to see Mercedes so far down the order.
