"I don't know if we can challenge, we're half a second behind today", the Briton told Sky Sports TV after aborting his final flying lap and taking fourth place on the grid with team-mate Valtteri Bottas in third.
"It was okay but not good enough", said Raikkonen after the session.
Verstappen - on fresher tires - ambitiously attempted to go down the inside of championship leader Vettel at Turn 14, hitting the German, who finished the race down in eighth with a damaged sidepod.
Reflecting on the performance, Hamilton admitted it was a case of underperforming on his side of the Mercedes garage, and that a solution needs to be found quickly if he's going to fight for a fifth title.
"I was quite good in that before but somehow this year with the previous two races going your way, you want to recover points and it's working against you at the moment".
The German lapped the 5.4-km Shanghai circuit in one minute, 31.095 seconds - a track record - to pip his Finnish teammate by a mere 0.087 seconds and take his 52nd career pole.
Mercedes team boss Toto Wolff revealed that making the tyres work was the problem.
"That would not be the right mindset", he said.
Valtteri Bottas said he felt in complete control of the Chinese Grand Prix before the Safety Car period which swung the race towards its eventual victor, Daniel Ricciardo. "The amusing thing about being outperformed on Saturday is that you are the lion that is just waiting to jump on its prey".
Daniel Ricciardo was the surprise victor of the Chinese Grand Prix as inspired tactics by his Red Bull Racing team and some ruthless overtaking gave the Australian victory in Shanghai. But does it really mean I have to calm down? "We definitely were not doing that for the cameras", said a clearly relieved Ricciardo.
"I'm thankful for a couple of incidents that happened ahead today, kept us kind of in the battle", Lewis added. "That will be fun".
Since Hamilton took pole position for the season-opening Australian GP, Ferrari have held a clear single-lap pace advantage over the world champions. I think he can do the same today. "It is a track where you just need to get in and find that sweet spot".
"I wouldn't be surprised if tomorrow that gap disappears and its a very tight race".
Saturday's pole was Vettel's second in three races this season and Ferrari's first in Shanghai since Brazilian Rubens Barrichello started the inaugural Chinese Grand Prix from the front in 2004.
Elsewhere, Renault's Nico Hulkenberg finished seventh, ahead of the Force India of Sergio Perez and Hulkenberg's teammate Carlos Sainz.