At the season-opener in Bahrain, Alonso qualified sixth but slipped to ninth behind the Mercedes and McLaren drivers in the race, finishing 74 seconds adrift of winner Max Verstappen.
Alonso qualified fourth for the Saudi Arabian GP, but he soon lost a place to Oscar Piastri's McLaren.
He then remained in fifth place for the duration of the race, successfully staying in front of the Mercedes of George Russell and finishing 35 seconds behind Verstappen.
After a disappointing race in Bahrain, Alonso agreed that Jeddah represented a step forward.
"I think it was better," he said. "We did introduce a new part on Friday that it worked really well. And I think we made a step forward in terms of performance.
"But we still miss maybe two or three tenths compared to McLaren and Mercedes, and we will keep chasing that kind of performance. It is challenging, but it's a nice challenge and an interesting season ahead."
He added: "Happy with the race result, in front of both Mercedes, one McLaren and one Ferrari. It's the maximum I think we can wish at the moment.
"We saw again in the race that we still miss two or three tenths compared to Mercedes and McLaren, maybe a little bit more compared to Red Bull and Ferrari. While in qualifying we seem pretty close. So yeah, we need to keep working on the race pace."
Source: Autosport