Gasly, who achieved his first victory in F1 powered by Honda at the recent Italian Grand Prix, said: "I have to admit I’m sad that Honda is leaving Formula 1 after the experiences we shared together.
"The people at Honda have played an important role in my career and I have always loved working with them.
"But we will still be together until the end of next year and I hope we can try and fight for more wins together before then, and that Honda will be in a position to fight for the championship title."
Gasly's win at Monza means Honda is the only power unit manufacturer to have helped two different F1 teams to victory.
Like the Frenchman, Kvyat is also disappointed to see Honda depart but has no doubt it will continue to give its all until the bitter end.
"I was surprised to hear the news that Honda will leave F1 at the end of next year," said Kvyat.
"It is sad on a human level as I enjoy working with their engineers, and disappointing from a racing point of view because they have worked so hard to give us the best possible power unit and we have seen it deliver some excellent results so far.
"The Honda guys at the track are really committed and I’m sure they will continue to push while they are still in the sport."
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