The Italian team introduced several parts of a major update to their 2012 car during testing at Mugello in Italy, where they made good progress.
"We will try to reduce the gap with the leaders at the moment because we were on average eight or nine-tenths off the top guys in the first four races," said Alonso.
"We need to reduce this immediately if we want to be in the fight for points and the championship.
"In Barcelona, we need to do the first step. We know there is no magic button that ensures that in Barcelona we will be on pole position because everyone will improve their cars as well.
"But we need to reduce this gap and Barcelona has to be the first step, Canada the second step and Valencia the third," he added with a nod to the two races lined up for June.
"Barcelona, for sure, is one of the most important steps that we have to do. We must do it. We cannot be fighting for Q3 (final qualifying) if we want to be fighting for the championship."
The two-time champion ran a new exhaust concept and rear bodywork on the final day at Mugello, but has played down the significance of what he tried.
He said: "Nothing surprising in terms of performance. I think we tried different configurations of exhaust layout and each day we had a different one and different parts on the car.
"I think it was just to confirm what our thoughts were and what to bring for the next races and for development. This year, it is not any more important what position you choose (for the exhaust system), or how you manage the position.
"We cannot lose even five minutes on this. There are bigger areas of the car where we need to improve and we are trying to do that.
"In a way it was a positive week and a positive test, because all the parts we put on, even if they were small in terms of performance, they worked as expected.
"So this has given us confidence for Barcelona, of bigger updates and future development. And now it seems we can trust the factory a little bit more!"
Alonso clocked the third fastest time on the final day of the Mugello test, despite an excursion off track in the morning which broke the car's front wing.
He ended up 0.328 seconds slower than pace-setting in-form Frenchman Romain Grosjean of Lotus. They were split by defending double world champion Sebastian Vettel of Red Bull.
The Spanish Grand Prix at Montmelo takes place on Sunday May 13.