Ferrari are cautious about their title chances despite a stunning first win of the season at the British Grand Prix.
Fernando Alonso benefited from improved race pace and a pit-stop error from Red Bull's leader Sebastian Vettel to win.
But Alonso, who is 92 points behind Vettel in the title race, said: "There are not championship thoughts because we know the gap is massive."
Ferrari team boss Stefano Domenicali added: "I want to be cautious but never say never."
Despite Ferrari's reservations the victory at Silverstone represented a significant step forward for the Italian team.
Alonso had led the Spanish Grand Prix in Barcelona but ended up being lapped by the Red Bulls and McLarens and the team responded by restructuring its technical department, with Aldo Costa stepping down as technical director.
Since then, Alonso has been on the podium in two of the last three races, in Monaco and Valencia, but promised the British race would be the real turning point.
"We brought quite a big aerodynamic update here and everything is working fine. Felipe [Massa] and I are feeling happier with the car," Alonso explained.
"It is no secret that we lost a bit of ground in the first couple of races because we put new parts on the car that weren't quick.
"But it seems that in the last three or four races every new part we put on the car is working fine. I am very proud of the recovery we have made.
"We just need to enjoy every weekend, try to win every weekend and be aggressive at the start, the pit stops, there is no time to think about any other thing."
Alonso passed Vettel for the lead in the second round of pit stops when Red Bull failed to attach his left-rear wheel properly. Alonso accepted the chance to storm clear and the Spaniard was uncatchable in the final phase of the race.
Alonso said: "Who knows what would have happened without the problem for Sebastian? It's not easy to overtake. The pit stop problem for them was a help.
"Here, with the track characteristics, high-speed corners and on the same tyres - the soft and the hard - we were much closer [to Red Bull]. It's definitely an improvement and we are much closer."
Domenicali also rejected suggestions that the win was a one-off earned only because of Vettel's mistake.
"Honestly today the race pace was good and so even without that problem, that we have suffered in the past, we could have won the race," he said. "Today we were very, very strong.
"We were expecting to be competitive. To win was a great result.
"It was a relief, for sure. It was important because after such a tough time it was a relief for everyone who has been working so hard for Ferrari."
Ferrari will go to the next race in Germany in two weeks' time confident that they are now Red Bull's closest challengers and with Alonso third behind the two Red Bull drivers in the championship.
Alonso recovered from a similarly poor start to the 2010 season to emerge as a title contender at the final race in Abu Dhabi, although last season a single driver had not built up a significant lead.
"It's a huge boost for us and we have good confidence being quick here at Silverstone," added Alonso, who is striving for his third world title.
"Winning here is good motivation and good confidence approaching the next races. We will enjoy the win and then work hard."
Alonso's victory came exactly 60 years after Ferrari recorded their first win in Britain thanks to a drive from Jose Froilan Gonzalez.
"The British Grand Prix is a special event for every driver competing in F1, we know the history of this race, a special grand prix and I had the privilege to drive the Froilan car that was the first Ferrari win in F1," said Alonso.
"Today we won in the same circuit with the same passion, the same group of people who work for this fantastic team.
"It was a very special day. Winning at such an historic and a fantastic circuit is even more special."
Alonso's victory means he leapfrogs McLaren pair Hamilton and Jenson Button to go third in the drivers' championship.