Neither of the former champions finished the race, but even before their retirements they had been unable to challenge for the top 10 and were being instructed to temper their performance in order to save fuel.
Alonso remained philosophical despite a third straight DNF - his worst run since coming into Formula One racing with Minardi in 2001 - but said McLaren cannot let up in their efforts to close the gap.
"Obviously, I'm a little bit sad to have suffered a third consecutive retirement," he said. "Definitely, we need to put some things in order - we know the situation for what it is but what we have to do now is work harder than ever because we want to change the situation more than ever.
"All the developments I know are coming for future races make sense, so I can see positive signs. I think we need to be patient now, and we need to continue to work incredibly hard.
"Hopefully we've learned a lesson, and it's better that all these problems are happening now, while we're not yet competitive."
Button described his Grand Prix as ‘quite painful’, but added: "I guess it's easy for people to look at today's result and say we're having a bad season, but that's not actually the case. We've made very big improvements since the first race, in fact.
"Yes, we're still quite a long way behind the other teams in terms of power unit development, and even the design philosophy behind our car too; but if you don't take a stab at it at the start of the season with a new project like this, you're never going to be able to fight the top guys."
McLaren-Honda racing director Eric Boullier commended the attitude of his two drivers, saying: "I want to take this opportunity to thank and praise both Fernando and Jenson, who are continuing to drive brilliantly in very trying circumstances, both of them digging deep and working extremely hard behind the scenes to help us move forward towards reliable competitiveness and eventual success.
"We know what we have to do to improve, and we're doing it. It may take us some time, but we'll get there."
McLaren lie ninth in the constructors’ championship after seven rounds, with the four points scored by Jenson Button for his eighth place in Monaco.