Ferrari fear their chances of fighting for the 2011 title will be over if Sebastian Vettel's charge for Red Bull is not stopped soon.
Vettel won four out of the first five races and leads Fernando Alonso, Ferrari's closest challenger, by 67 points.
Team boss Stefano Domenicali said: "If Red Bull keep progressing, then no doubt it (the title) will not be easy.
"They are very far ahead. We know it is difficult, but we don't give up."
Vettel claimed his fourth victory of the season at the Spanish Grand Prix despite increased pressure from his rivals at McLaren and Ferrari.
Alonso led the race for 18 laps after a sensational move from fourth on the grid but he crossed the line in fifth because his Ferrari could not match the pace of his rivals over the full race distance.
Alonso also suffered the ignominy of being lapped by the faster cars of Red Bull and McLaren while his team-mate Felipe Massa retired.
Domenicali has pointed to the next two grands prix, in Monaco on Sunday and in Montreal two weeks later, as the acid test for Ferrari to renew their challenge.
"We need to be very cautious and see where we are in the next couple of grands prix because we will have much softer tyres and a different configuration of the track," said the Ferrari team principal.
"Then we will see where we are in terms of fighting for the title.
"We need to make sure we do the maximum to recover. The nature of the people in Maranello has to be that they need to push and to work hard because we want to keep it alive as long as possible, so we still believe."
Ferrari's attempt to close the gap in Barcelona was hampered when the sport's governing body, the FIA, ruled that their new rear wing did not comply to the rulebook.
But Domenicali and Alonso also blamed the Italian team's disappointing performance on the car's inability to get performance out of the harder tyres.
"We lost around two seconds per lap, which is really difficult to explain," added Domenicali.
"Unfortunately the tyres were unable to work on our cars which were sliding around because we could not get any temperature into them.
"Sunday was the worst race we have had since the beginning of the season in terms of race pace because before that we were quick, so it's a shame."
Alonso had to run two race stints on the hard tyres in Spain after sacrificing a set of soft tyres to qualify in fourth.
He added: "[We did] half the race on the hard tyres, which penalised us heavily and made the gap bigger than it is in reality.
"But in the space of two weeks we have lost ground to Red Bull and McLaren, and we have to understand why.
"I am definitely not thinking of giving up on the championship after just five races."
Tyres will again be a key issue around the twisting streets of Monte Carlo as, for the first time this season, Pirelli are supplying the supersoft tyres along with the soft tyres used at the first five races.
The supersofts should suit Monaco's slower street circuit but are not expected to last as long, which will again present the teams with strategy headaches.