McLaren had been bullish ahead of the British round of the championship, believing upgrades to the MP4-27 would lead to a strong performance on home soil.
But after starting eighth and 16th respectively the pair were never a factor in the fight for the podium places and ultimately finished down in eighth and 10th positions as Mark Webber secured victory for Red Bull.
On the evidence of the last two rounds, here and at Valencia, McLaren are some way off the pace of Red Bull and Ferrari and Hamilton, who has now fallen 37 points behind championship leader Fernando Alonso, knows there is plenty of work to be done before the German Grand Prix.
When asked how far the team are behind Red Bull, Hamilton said: "A long way away, but we will keep working at it and hopefully catch them up.
"It wasn't a special race to be honest, I wish we could have done more for the fans, we tried as hard as we could but we just didn't have the pace today [Sunday].
"I don't know why. I think I was in the lead at one point so I don't understand how you can be there and then go all the way back back to where I started, but I pushed all the way and did everything I could.
"I was flat out right to the end but for some reason we didn't have any speed."
Hamilton also said he would take a look at the strategy McLaren used for him on Sunday.
Hamilton started on the hard compound tyre and took the lead when those ahead of him stopped, but as his tyres started to go off Alonso easily caught and passed the McLaren.
But Hamilton felt he could have stayed out longer, even though he was substantially slower than the leaders immediately prior to his stop.
He said: "From what I can understand it must have been okay, but I will have to look at it afterwards to see how the strategy panned out.
"In the first stint my tyres were still good and I was almost holding on to Fernando on quite old tyres so maybe a one stop (strategy) would have been possible, I really don't know to be honest.
"We did everything we could but it was a really tough race for us, really tough."
Button, now without a podium finish on home soil in 13 attempts, was similarly despondent, and believes that it is not just the Red Bulls and Ferraris who have got the McLarens beat on pure speed at the moment.
He said: "I just don't think we are very quick at the moment. I think that's an issue for both cars.
"The Red Bulls look strong and even following the Williams around you can see they are very strong. They can put their car in certain areas I could not imagine putting the car and getting away with it.
"We have to find some pace, it's not just Red Bull and Ferrari that are quicker than us, I think a lot of cars are, I just don't think they got their strategy right today.
"We have a lot to work on and I am sorry to the fans we could not have a better result and fight at the front, hopefully we can do that soon."