Alonso struggled throughout the opening week of practice at the Indianapolis Motor Speedway and slipped into Sunday's Last Row Shootout after failing to secure a top-30 spot. Over the four-lap averages, Alonso was bumped from that showdown by American Kyle Kaiser by just 0.019 mph.
De Ferran, winner of the 2003 Indy 500, worked with Alonso during his debut in a McLaren-Andretti Autosport partnership at the Brickyard in 2017, before being given his current role with McLaren.
The British team built its own team for this year's attempt, headed up by former Force India deputy principal Bob Fernley, who was confirmed to have left the team on Monday.
This year's entry was seen as a precursor to a full IndyCar season in 2020 for McLaren. Instead, de Ferran spent Sunday evening saying sorry to everyone involved in the project for failing to make the grade.
"This has been a very emotional and difficult experience, not only for me but for the whole team," de Ferran is quoted as saying by Racer. "I want to take this opportunity to apologise and thank the fans, not only here in the U.S. but globally, who have been following our progress. I read a lot of nice things and some great messages all over the place. So thank you, and I'm sorry we won't be in the Indy 500."
After also apologising to McLaren's Indy 500 team and to its sponsors, de Ferran spoke to the man seated alongside him: "Last but not least, I want to thank this man here on my left -- I want to apologise to you, as well, because we didn't give you a car that was fast enough. You drove like the champion that we know you are.
"Particularly these last three days have been incredibly tense and very difficult, and we couldn't have asked anything more from you, Fernando. So I'm sorry, man. You're an amazing driver. In my 35 years of racing, actually a few more, this is the most painful experience I've ever had.
"There's a mixture of emotions going on inside of me, but we are racers. We respect this place. This is one of the toughest challenges in racing. I want to come back tomorrow. I want to fight. I want to come back tomorrow and fight. This is incredibly painful."
McLaren has also confirmed it will not seek to buy another team's entry on the grid in order to get Alonso a place in the race, an option that is open to anyone who fails to qualify.
"We want to earn our place in the field," de Ferran said.
Alonso's failure means he will need to wait at least another year before attempting to claim the final piece of motor racing's Triple Crown -- he already has victories at the Monaco Grand Prix and the Le Mans 24 Hours. Alonso is aiming to become only the second driver to claim that triple; two-time world champion Graham Hill did so in the 1960s and 1970s.