A largely quiet race looked set to peter out to a slow conclusion with Red Bull on course for a long-awaited one-two finish before Max Verstappen suffered a left-rear tyre blowout that shunted him into the wall at around 200mph.
That was with just four laps remaining and the race was red-flagged to allow the Baku track to be cleared, before a standing restart granted Hamilton the chance to jump Perez.
But while the seven-time world champion got away well, he locked up into turn one and went into the run-off area as Perez ran clear for victory ahead of Aston Martin’s Sebastian Vettel and AlphaTauri’s Pierre Gasly.
Hamilton got his car back on track but could only finish 15th, while team-mate Valtteri Bottas ended in 12th as the Silver Arrows ultimately endured a forgettable race day.
The Briton had been on to overtake title rival Verstappen in the Drivers’ Championship but remains four points behind while Red Bull have 178 points to Mercedes’ 148 in the Constructors’.
But Wolff insists Hamilton is not to blame for what happened as he opened up on the problems facing Mercedes up against their Milton Keynes-based opponents.
Wolff told Sky Sports F1: “It can’t be called a mistake. It was just when Sergio came over, he touched a button and the brake balance changed.
“The brake balance went all the way forward and ultimately the car couldn’t stop.”
The brakes on Hamilton’s W12 poured with smoke before the restart, but Wolff said: “I don’t think that was the problem. I think it was more a simple, how can I say, finger problem.”
The Austrian continued after back-to-back Red Bull race wins: “In Monaco and here, we didn’t have a car that was competitive.
“We still have our underlying issues that we’re not getting off the start into the happy window of the tyres with the set-up.
“And also after the stops we make operational mistakes and we lose all the time that you can see today in the twisty old town and city. This is what happened in Monaco.
“It’s not a shocker now that the car that won three races is nowhere. It is not. We know the deficit, we’ve seen that in these particular parts of the tracks.
“We know that we have gaps that we just need to overcome. The 90-degrees corners we’ve actually been quite competitive. It was all the twisty bits, seven to 10, you could see in the middle sector we were really close, it was quick on the straight but the middle sector was a total shocker.”
Wolff made it clear that he would pick no other driver over Hamilton, with whom Mercedes have won seven straight Constructors’ Championships, the reigning world champion picking up six of seven driver’s titles in that time.
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“We have four hours together on the plane now. Maybe we’ll drink,” the Mercedes boss continued. “Maybe that’s not good to say on Sky but we will drink.
“He just doesn’t make any mistakes. That is what you need to remember. I wouldn’t wish for anybody else to be in the car.”
And Wolff insists Mercedes are confident of bouncing back with F1 headed to France next up on the weekend of June 18 to June 20.
He said: “We have no doubt. It’s a team that is so strong and so angry. We’ve got to transform the anger into positive force. We’re warriors and we’re going to come back.”
While Wolff also explained of the struggling Bottas: “The car was nowhere. When the car is nowhere in a city circuit, you lose all confidence.”