In Florida, Alonso dropped out of the points when he was handed a penalty for gaining an advantage by going off track when battling with Mick Schumacher.
Although such penalties cannot be challenged, Alonso and Alpine sporting director Alan Permane went to see the stewards after the race in order to state their case.
Sources have indicated to Autosport that, while Alonso did try to give back the time he had gained, there was a bigger picture at play.
In going off track, he had gained an advantage by dropping Schumacher out of DRS activation, which also put the German under threat from Esteban Ocon in the other Alpine.
In Barcelona on Friday, Alonso made his frustration clear, accusing the stewards of “incompetence”.
He subsequently had a talk about the matter with Ben Sulayem, who is keen to improve the championship’s race direction and stewarding system.
“I speak with him regularly,” Alonso said after qualifying in Barcelona. “He knew my feedback after Miami already.
“So he was aware of everything. At the end of the day, we are all trying to help each other you know, the FIA, drivers, GPDA, we are all in the same boat, and we try to make the sport more fair and better.
“So I think it was a nice and friendly talk, and we will move forward and hopefully get better and more consistent.”
When asked if he had apologised for his earlier comments Alonso grinned, implying that he hadn’t.
Alonso got involving in a misunderstanding in qualifying with McLaren’s Lando Norris
Photo by: Carl Bingham / Motorsport Images
Alonso will start his home race on Sunday from the back of the grid after Alpine opted to change his Renault engine on Sunday morning.
But, even before his engine change, Alonso believed that only a “mega fantastic safety car” would allow him to make progress after being left 17th during a frustrating qualifying session.
“I think there is not much you can do,” he said. “This is Barcelona, not much overtaking, a lot of tyre degradation when you run behind cars. So let’s see.
“If I have one of those mega fantastic safety cars in the right moment maybe I get lucky, and I take couple of points, but I doubt it. I think it’s going to be a difficult race.”
His final run in Q1 was compromised by what he called a “misunderstanding” with his team over the time available to beat the chequered flag at the end of the session.
Alonso stayed closer to the car of Lando Norris than was optimal only to find out that he had extra leeway and could have dropped back and given himself more space.
“It was a misunderstanding in quali,” he said when asked about the session by Autosport. “Because I started the lap behind Lando thinking that I had one or two seconds margin with the red light, but then I had like 20 seconds margin.
“So if I knew that in advance I will create more gap with Lando and do my own lap. I heard in the radio it’s very tight, you need to go now, now, now, so I went immediately when they told me, and it was not necessary at the end.
“So that was a misunderstanding obviously with a high price because Barcelona, if you start at the back, everything becomes more difficult.”
