The Red Bull driver said at a news conference Thursday before the Canadian Grand Prix that he's exhausted of questions about the crash in Azerbaijan that also knocked out teammate Daniel Ricciardo, or the one in Monaco that sent him to the back of the grid.
Vettel was delighted with his lap, which was Ferrari's first pole in Canada since 2001.
However, Hamilton refused to blame that for his deficit to his rivals: "I don't think today's performance has got anything to do with the older engine".
Having threatened to "head-butt" someone on Thursday after getting irritated by persistent questions about his many crashes this year, Verstappen was satisfied with his qualifying run.
"I'm getting really exhausted of all the questions", said the 20-year-old, who has fewer than half the points of Red Bull team-mate Daniel Ricciardo ahead of Sunday's Canadian Grand Prix. "The vehicle was working well, but we are still lacking a bit of top speed and you could see that in the long runs".
However, despite recording his first non-front-row start in Montreal for seven years, Hamilton insisted: "I'm hoping tomorrow that we're still in a good position".
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Vettel powered his Ferrari around the 4.361-kilometre Circuit Gilles Villeneuve in one minute 10.776 seconds. There was a little bit more, but I'm still happy.
In a closely-fought qualifying session amongst the top three teams, Vettel rose above the parapet to clinch his 54th pole position, beating Mercedes' Valtteri Bottas to the top spot by less than a tenth of a second.
On a dry and sunlit day, there was immediate drama when Romain Grosjean pulled up in the pit-lane with clouds of smoke billowing from his Haas car's Ferrari engine. "I think we need a little bit more time to get everything together and then we'll see where we are".
Hamilton leads Vettel by 14 points in the championship heading into the weekend, with Ricciardo third, 38 points off the lead.
When asked if he felt Red Bull had the pace for pole after seeing teammate Daniel Ricciardo go quickest in Q2, he said: "I knew we had a good auto, but I wanted to wait and see how competitive we would be in Q3".
The young Dutchman Verstappen clocked 1:12.198 seconds.
Mercedes were first out in Q3 and smashed the records, Bottas topping Hamilton in 1:10.857 before Vettel beat that.