(CNN) -- Bernie Ecclestone had called it "unacceptable," while Ferrari's president chimed in on the lack of engine noise and apparent "taxi driving" enforced by fuel restrictions -- but Formula One delivered what its fans most want on Sunday.
Pure racing. The exhilarating sight -- if not sound -- of drivers overtaking and pushing the limits.
While, like last season, there is clearly one dominant team -- this time Mercedes -- the introduction of new design rules and the smaller, yet seemingly more powerful turbo engines has added an element that had been lacking when Sebastian Vettel's Red Bull dominated so comprehensively in 2013.
"I strongly dislike coming second to Lewis, but on the other hand that was the most exciting race I've ever had in my career," Mercedes' championship leader Nico Rosberg said after being beaten into second place in Bahrain by Englishman Hamilton.
"Today was a great day for the sport, and hopefully you had a lot of fun watching on television."
Hamilton triumphed by just over three seconds, having overtaken pole-sitting teammate Rosberg at the start but then being hauled back by the safety car following a collision between Lotus' Pastor Maldonado and Sauber's Esteban Gutierrez. The Mexican escaped unscathed despite his car's spectacular somersault.
"It was exciting. Nico drove fantastically well, very fair, and it was hard to keep him behind at the end," said 2008 world champion Hamilton, who moved up to equal 10th on the all-time victories list with the 24th checkered flag of his career.
"I was on a knife edge the whole time. It was a relief when I crossed the line."
The childhood friends and rivals have dominated this season, winning all three races and claiming all three pole positions -- Rosberg now has an 11-point advantage at the top, with Nico Hulkenberg a further 22 back from Hamilton in third.
It has been a big turnaround for Mercedes, which finished second in last year's constructors' standings -- a massive 236 points behind Red Bull.
But the German manufacturer has adapted best to the new rules -- reflected in the Mercedes-powered Force India claiming a surprise podium placing at Sakhir as Hulkenberg's teammate Sergio Perez came in third, some 23 seconds behind Rosberg.
Red Bull, struggling this season with its Renault engines, did manage fourth place as Daniel Ricciardo upstaged Vettel by overcoming the 10-place penalty that put him 13th on the start grid.
Hulkenberg was fifth in a notable double for Force India, ahead of his fellow German and four-time world champion Vettel -- winner of the past two races in Bahrain.
Mercedes-powered Williams took seventh and eighth through Felipe Massa and Valtteri Bottas respectively.
Massa's former Ferrari teammate Fernando Alonso came home in a disappointing ninth, disconsolately punching the air in irony as he crossed the line ahead of new colleague Kimi Raikkonen.
McLaren, also powered by Mercedes, had a disappointing outing as 2009 world champion Jenson Button retired two laps from the end in his 250th race while rookie Kevin Magnussen -- second in the season opener and ninth in Malaysia -- quit after 40 of the 57 laps.
Maldonado was given a five-place penalty for the next race in China and three points against his Super Licence after hitting Gutierrez on lap 41.
Marussia's Jules Bianchi was given two penalty points -- a total of 12 means a one-race ban -- for ending the race of Gutierrez's Sauber teammate Adrian Sutil, who has a five-place penalty for China after an infringement in Saturday's qualifying.
The F1 caravan will head to Shanghai in two weeks with the sport's chief executive Ecclestone demanding changes after criticisms over the perceived lack of atmosphere at races.
"People buying tickets are expecting to see what Formula One used to be, and as I've mentioned before, I've had letters from promoters," the 83-year-old told reporters in the paddock before the Bahrain race, which was celebrating its 10th anniversary.
"They're all worried if they lose spectators then they are going to be in trouble.
"What is important is that the teams know the problem, the engine manufacturers know the problem, and they're trying to sort it."
Ferrari president Luca Di Montezemolo also voiced his concerns.
"I don't want to think of the decline of Formula One, and if we look at it today, we have a race that is no longer Formula One," the Italian said before the GP.
"We have to give back to Formula One its characteristics. We cannot have an economy formula. It has to be extreme, with racing from the first lap to the last.
"Formula One is also about the engine music -- not noise -- and we also have to make sure it is not too complicated with regard to the rules."
However, the head of motorsport's governing body said the 2014 changes had been necessary due to "environment legislation" which was restricting the use of circuits for F1, and said teams had to adapt to the new challenges.
"If you ask Hamilton and Rosberg if they are driving like taxi drivers ... if you have an efficient car you don't have any problem," said FIA president Jean Todt, formerly team boss at Ferrari when Michael Schumacher was the dominant force of F1.
"It seems Mercedes is stronger. I don't have the power to say 'Let's slow them down.' If they are quicker than the others I think it is a challenge for the other teams to catch them.
"It is completely unfair to punish a team who has been doing a better job."