Ferrari are concerned by the pace Sebastian Vettel showed at the European Grand Prix before his retirement.
Ferrari's and the championship lead after Vettel's Red Bull stopped with alternator failure.
Ferrari team boss Stefano Domenicali said: "They did something very good this weekend; they improved the car.
"We are not at the level we should be in terms of performance. Red Bull was the quickest."
Alonso now leads the championship by 20 points from Red Bull's Mark Webber, with McLaren's Lewis Hamilton third and Vettel fourth.
The Spaniard became the first man to win two grands prix so far this season, which until Sunday had seen seven different winners in the first seven races.
But Red Bull have been on pole position for the last three races - and four of the last five.
And the car took an obvious step forward in performance in Valencia following a major aerodynamic upgrade, Vettel taking pole position by 0.324 seconds before lapping about a second a lap faster than anyone else throughout the race.
Alonso and team-mate Felipe Massa, meanwhile, qualified 11th and 13th after a tactical error by Ferrari.
Dominecali said: "We will never be happy until we are in pole position. We are fighting to improve the car.
"We cannot be happy because we are not there at the moment. We need to keep our feet on the ground but this is a very different car from where we started the season."
Ferrari started the year with a car more than a second off the pace but steady improvement and some determined and impressive races from Alonso have kept them in the championship picture.
Domenicali praised Alonso after the race in Valencia, in which he pulled off a series of brave overtaking moves to put himself in contention before Vettel's retirement.
"We know he is the number one driver and that is the reason why he is here with us," Domenicali said.
"I'm very happy for him today because he had such pressure [in his home race].
"I was so happy to see him in this fighting mode and the team was supporting him with the right moves.
"We need to stay calm and cool. Our main competitors had some problems. Reliability is a key factor, we need to score points every time.
"Things can change very quickly and it is important to stay focused."
Alonso added: "In qualifying we were eleventh and thirteenth so we need to work.
"We will have confidence in ourselves and arrive with optimism at every Grand Prix we go to.
"At the same time, apart from winning or finishing sixth (with Massa), we know that we are not in the position that we want to be. There are a few cars quicker than us and we cannot be blind to that. We need to work."