Vettel is 36 points clear of Alonso in the title standings, with the campaign not yet at its halfway point.
But despite the widening distance to the leader, Alonso believes that nothing is lost just yet, and reckons Ferrari can still turn things around over the remainder of the campaign.
"Being 36 points behind the leader, we don't have much more room to make mistakes or lose many more points," said Alonso ahead of this weekend's British Grand Prix.
"But on the other side we need to remain calm and do our job. If we can win races and if we can finish in front of Sebastian it will be great, but if we cannot, then we try and lose the minimum points.
"Last year I had an advantage around Monza time of 42 points, and it was not enough. So being the eighth race and 36 points behind is not an ideal position, but it is not the end of the world."
Alonso thinks Vettel's advantage in the standings has been particularly boosted by the fact that both he and Kimi Raikkonen have endured two lacklustre grands prix, while their Red Bull rival has been strong everywhere.
"I think he [Vettel] is doing a fantastic job in all the races," he said. "He has been nearly perfect with no down races, always performing well in qualifying and with very good races.
"Obviously I had two unlucky situations, one in Malaysia and one in Bahrain. Kimi was leading the championship and then was very close until he had two unlucky situations, one in Monaco and one in Canada which was a mixed race for him.
"So we need to keep fighting, we need to keep pushing to recover now these bad races we have had.
"Red Bull is improving really well, compared to the first part of the championship. We need to raise our game if we want to arrive at him."
Alonso is one of the favourites for success at Silverstone this weekend, with his Ferrari having excelled on high-speed tracks so far this year.
And although conceding that nothing can be taken for granted - especially with tyres playing such a key role this year – he says there is a level of confidence at the team.
"It should be a good circuit for us," he said. "We have been more or less competitive here for the last three or four years, and it is the first circuit that is similar to China and Barcelona, which have been the best circuits for this year's car.
"We have some high hopes for this weekend. But, on the other hand, Red Bull has been quite strong and dominant here since 2009, so it will be a close and challenging weekend - with Mercedes as well who I am sure will be very, very strong as well.
"We have an interesting weekend ahead of us, but we can approach it with confidence, knowing we have a good opportunity."
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