(By Paul Virgo) Rome, September 10 - Ferrari and Fernando Alonso still believe in their bid to end Sebastian Vettel's dominance of Formula One even after finishing second to the German world champion at their home grand prix last weekend. Alonso gave a trademark combative display at Monza last weekend, but he could do no more than limit the damage and make the second rung of the podium, with the speed gap between Vettel's Red Bull RB9 and the Spaniard's Ferrari F138 too big. That meant Vettel, who is bidding for a fourth consecutive world title, extended his lead over Alonso in the drivers' standing to 53 points with seven races to go. Ferrari are also second in the constructors' table, 104 points behind Red Bull. "We'll believe right until the end," Alonso told fans via his Twitter account @alo_oficial. "We'll be giving our all". The 32-year-old, who won the 2005 and 2006 world titles with Renault, also reiterated he was happy at Ferrari and committed to staying with the Italian glamour team. Reports that Alonso could leave Ferrari, with whom he has contract until the end of 2016, and join Red Bull resurfaced after he seemed to call the team engineers idiots over the team radio in qualifying on Saturday. But when asked what Ferrari meant to him on Monday, he replied: "it's a way of living, my team, my second family, my friends". Ferrari President Luca Cordero di Montezemolo hit an optimistic note on Tuesday, with Ferrari set to introduce changes to the car that they hope will boost performance at the Singapore Grand Prix next week. "We're looking forward, there are still lots of races to go," Montezemolo told reporters and the Frankfurt Motor Show. "We mustn't give up". He also thanked Ferrari's fans for sticking by the team in the recent trophy-less seasons, but stressed that he would have liked to have heard fewer boos directed at Vettel after he won at Monza on Sunday. "The fans have shown great affection and understanding and this must drive us to do even more," he added. "In recent years, Ferrari have always been near the top, but I'm not happy to see us unable to win at Monza. "We need everyone's effort. We need a more competitive car". Montezemolo refused to talk about Ferrari's driver line-up for next season, amid reports they are about to drop Alonso's Brazilian teammate Felipe Massa and bring back Kimi Raikkonen. The Finn, who is currently competing for Lotus, was the last man to win the driver's championship for Ferrari, in 2007.