Ferrari was well off the pace in the first three races, but appeared to make a step forward in the recent Chinese Grand Prix, where Alonso scored the Scuderia's first podium since the Brazilian finale of 2013.
Alonso remained cautious about hailing the Shanghai race, in which he ran as high as second and beat both Red Bulls, as a breakthrough for his team.
He reckons Ferrari will have to work harder than ever to make significant steps forward with the F14 T compared to its rivals.
"The car was under-performing in many areas - it was not just one problem," Alonso explained.
"We need to be more efficient, have better aerodynamics, better traction, better power. We lack some big performance in the first races.
Gary Anderson's trackside F1 verdict
"[in China the improvement] was nothing really big in one area, just small steps here, small steps there - better power delivery, better software, putting everything in place, all the settings, and giving a little bit more aero efficiency and a little bit more power.
"We have bigger margins, because we started in a lower performance, but we cannot dream too much because people will not be watching TV from here to Barcelona.
"The other teams will bring a couple of tenths to Barcelona, [so] we need to bring a couple of tenths, plus something, if we want to catch up.
"That's the challenge we are facing now. It's not that we need to develop the car at a normal rate; we need to do the normal development, plus something."