Esteban Ocon started and finished third in the principality, while Gasly took seventh despite being frustrated by making a stop for dry tyres shortly before the rain came.
The Monaco performance came after disappointing weekends for the team in Bahrain and Baku, and the ensuing public criticism from Alpine CEO Laurent Rossi.
"I'll say I see more smiles," Gasly said when asked by Motorsport.com if he could already sense a more optimistic mood. "Usually from past experience, the more people smile, the more efficient they get.
"So I must say I'm pleased for the entire team that we managed to get that result, that it managed to get some weight off their shoulders.
"I don't believe that is going to change anything in their approach, because we're all fighting, we're all pushing to get every everything out of the car that we got.
"Surely, I think it was a general feeling inside the team that we feel like we were not performing as much as we would have hoped at the start of the year.
"And the fact of seeing progression, evolution through these first Grands Prix can really probably like click and kick something within the team in terms of mindset, in terms of confidence, moving forward."
Gasly says that there has been a genuine improvement in the form of the A523 thanks to development parts and a better understanding of how to optimise the car.
"I think there are so many parameters that come into play," he said. "We obviously brought new parts in Miami, we had the new upgrades coming in Imola, which we didn't use there, but which we obviously used in Monaco, which made the overall performance better.
"There is more understanding on what's good in the car, what's slightly less good.
"A weekend like Baku was definitely not great to go through, but also we understood more about the package that we had, which made us make different decisions for Monaco, which ultimately helped us to get the result that we had in Monaco.
"So I just feel weekend after weekend we're able to have a stronger package, more consistent, more reliable, more compliant, and more robust."
Ocon agreed that the Monaco result was a huge boost for the team after some weeks of frustration.
"It was clear that we were not happy with how the season had started," he said. "We were struggling and not scoring as many points as we needed to.
"But we never stop believing, working the way we should to try and get that car as high as it can go and nothing has changed from that. Everyone was giving the maximum for that to happen."
He added: "Everyone at the team deserved what happened last weekend.
"All the hard work has paid off and it shows that we can be there and it gives everyone more hunger to keep going, now that we've tasted it.
"We always need to aim to make it happen again so I'm hoping it's the first of many this season. But that's what we need to look at, I'm not saying that's what's going to happen.
"I'm trusting the plan of Laurent Rossi and [Renault CEO] Luca de Meo. They are very competitive people and I'm fully onboard with the 100 races target plan that they have."
