The German world champion started Sunday's race in pole position and despite having a clean start, made an error through turn two - running wide and allowing eventual winner Jenson Button to take the lead with ease.
Despite chalking up another 18 points to stretch his lead, Vettel is urging his team to push harder to fend off the increasing competition from McLaren.
"Second is an important step, but the win was in reach and we did not get it," said Vettel.
"The McLarens have made a step forward, and now we have to make a step to regain the advantage.
"We need to come back and we will be pushing hard for Spa."
Button expressed his delight in capping his 200th Grand Prix with a win
"It's good we've a couple of weeks' break now because it might take me that long to get over tonight," he said.
"But I won my first race here in 2006, again here, so this is a great moment.
"I like these conditions. I don't know why, but it was a great call by the team to switch to the prime tyres (at his third stop) rather than the inters (when the rain was again falling).
"But everyone has worked so hard, and although we go into the break on a high, we'll be thinking of Spa (next race in Belgium at the end of August) and we'll be ready to go again."