Verstappen missed out on a shot at pole position after making a mistake in Turn 7 on his first flying lap in Q3 and then missing out on a second attempt due to a red flag at the end of the session.
Without a Q3 lap time to his name, he will line up ninth on the grid while Red Bull teammate Sergio Perez starts from pole position.
Asked what result was possible in Sunday's race, he responded: "Minimum is P2."
Verstappen was unable to complete his second attempt in Q3 due to the session being suspended by a red flag with 96 seconds remaining after Charles Leclerc crashed at Turn 7.
The Ferrari driver's mistake deprived Verstappen of another shot at the pole, but he said he still took the blame for his lowly starting position.
"Yeah, of course that [the red flag] is unfortunate," Verstappen said. "But first of all, we didn't do a lap and that was my fault. It was extremely tricky.
"I was a little bit off line out of [Turn] 6 and into 7. I felt a bit of understeer and I just couldn't get it back in the line. So I aborted my lap and then of course you need a bit of luck, of course hoping that there won't be a red flag.
"Of course, when you try to think like that, then it happens. It's a bit upsetting. The whole weekend we have been pretty quick, my Q2 lap was fast enough for pole in Q3.
"I guess that says that we have a quick car but you need to put it together, and when it matters, we didn't. That's a bit frustrating from my part."
Saturday's qualifying result builds championship momentum behind Perez, who won last weekend's Azerbaijan Grand Prix to draw within six points of Verstappen in the championship.
But Verstappen seemed unfazed about the prospect of falling behind his teammate in the standings on Sunday.
"It's not a great day, but the championship isn't won tomorrow," Verstappen added. "I've been in this position before, you have sometimes a few setbacks but that doesn't mean that it carries on for the rest of the year or whatever.
"It can't always be perfect, you hope that it's going to be perfect. Last year we had a tough start, but you still need to nail a few bits yourself. Today was not great."