Ten rounds into the 20-race FIA Formula One World Championship, Haas remains seventh in the constructors standings with 29 points but only three points ahead of eighth-place Renault, which earned eight points via Hulkenberg's sixth-place result.
"There is still work to do to get the vehicle more drivable and to be able to trust it more in the high-speed corners", Bottas said.
Raikkonen said he was disappointed with his misfortunes, but Vettel said he did not blame the team.
Vettel qualified third but was 0.756secs behind his championship rival, with Valtteri Bottas fourth fastest but starting from ninth due to a five-place grid penalty. I think the time he put in at the end was very strong.
Verstappen was involved in an amusing moment of team radio when his engineer warned him about yellow caution flags at Turn Seven, only for Verstappen, who had just run wide at the corner, to reply: "Yes, because of me".
"Thank you to everyone who turned up, I see you, God bless you", said Hamilton over the radio on the cool down lap before stepping out of his vehicle to chants of "Lewis!"
Vettel, whose brakes were smoking before the start, lost third to Red Bull's Max Verstappen. Vettel, who appeared to have benefited from his teammate's misfortune, suffered a puncture only a lap later, his auto dragging along the ground and throwing up sparks as it crawled back to the pits.
For the larger part of the grand prix, Raikkonen was able to live up to his nickname "The Iceman" as once Lewis got rid of him off the line he was running a pretty easy race in second.
Raikkonen needed a late tyre change which appeared to promote Vettel to the podium but disaster struck for the four-time champion on the last of 51 laps.
The Finn tried to pass him on lap 42, when Vettel defended his position, but succeeded a lap later by surging past on Hangar Straight into Stowe as the German's tyres faded.
Vettel's tyres developed blisters, as happened with other drivers on the grid including Hamilton, but it was Raikkonen who suffered a failure on his right-front tyre first.