Wolff believes the team will regroup in time for its home race at the German Grand Prix.
But he surged back into contention and thanks to the safety vehicle being deployed on two occasions late on in the race surged into second place.
The Englishman clearly blamed Raikkonen, who was handed a 10-seconds penalty, for the crash and found it hard to face the Finn or accept an apology.
The win was Vettel's fourth of the season, 51st of his career, and once-dominant champions Mercedes' first defeat at Silverstone since 2012 before the V6 turbo era started.
"I'm happy first of all for the team", the Italian told Channel 4.
But spurred on by a record 140,000 race-day crowd, the home favourite drove superbly to race back to second place and said on Twitter afterwards he "used every ounce of energy fighting up the grid". This morning he had a lot of treatment and to be honest, before the race I was really very concerned about him but today he fought like a lion.
Hamilton rushed back into the mix for a podium spot with the majority of runners picking a one-stop strategy until Marcus Ericsson lost control of his Sauber at Turn 1, and his fierce shunt into the tyre barrier brought out a lap 33 safety vehicle.More news: 5 things to know about Amazon Prime day
"Dead last to P2, that's an awesome effort", Mercedes told Hamilton.
Hamilton managed to fight his way back to finish second after a Ferrari-Mercedes duel developed with Valtteri Bottas leading until Vettel hit the front again with five laps to go.
Vettel ended up taking top spot, with Hamilton in second and Kimi Raikkonen in third.
"The reason Lewis didn't talk to me in the Parc Ferme is because he wanted time to go and calm down", Brundle explained to Sky Sports.
"My team did an wonderful job this weekend, we got so much support".
By turn three Kimi Raikkonen was lining up the Briton to take advantage of his tardy getaway, but the Finn locked his front-left wheel and smacked into the side of the Mercedes, knocking it off the road and sending Hamilton tumbling down the order. "Sometimes we say dumb s**t and we learn from it".
"It was my mistake".
Lewis said: "That lap took everything out of me, it was the toughest lap I've ever had to do in a qualifying session. If their tussle has been largely civil so far this season, the ill will brewing between F1's two most dominant teams suggests that battles in the 11 races to come could be anything but". Frenchman Esteban Ocon finished seventh for Force India, who are now level on points with McLaren and ahead on podiums.