Spaniard Alonso has struggled with Honda power for the last three years, but now McLaren are switching to Renault customer engines.
"We hope they find a new energy with the Renault engine," F1 chief executive Carey told Corriere della Sera newspaper.
"Alonso is a driver we all admire and follow. Last year was very hard when he exited in Russia on the warm-up lap."
Carey also said that he backs the Ferrari team, even though he is locked in a dispute with the Italian outfit that is threatening to quit the sport.
"Ferrari has a unique importance and is a legend, but it must be treated like all the other teams," he insisted.
"We want them to remain part of the category - we want to change the sport for the better, not change the teams.
"Agreements can be reached, but the main objective is non-negotiable - the interest of the fans comes first.
"We have to improve the show we offer on the track. The aerodynamics do not help and I am told that it is also a problem of some of the circuits."
Overall, Carey said that he is happy with how Liberty Media's first year in Formula 1 went.
"In the beginning, the priority was to look at the organisational parts, and we did that," he said.
"Then we wanted to give a fresh air to the environment, as only negative things were being heard - like when Bernie said he would not spend money to watch a race.
"Now everything is more open, there is a lot of social activity, ticket prices have gone down and we have created entertainment areas for the fans. All that accelerates the change."
The new season gets underway in March.