Domenicali resigned on Monday, with Ferrari having struggled for pace in the season's early races.
Alonso is already 35 points behind the drivers' championship leader - Mercedes' Nico Rosberg - but the Spaniard expects his team to respond in Shanghai.
"There has been some news from the team and we're here to try to improve the situation a little bit," he said.
"(We have to) be a little bit more competitive, more than we have shown in the first three races. We're here to fight back.
"It's not where we wanted to be. I think there is a lot of room to improve. We need to become better in all the areas from the car.
"There is a long way to go, the championship is very long and we know that probably in the first (part) of the championship we will not be as competitive as Mercedes or some of the teams that now are on top."
Domenicali has been replaced by Marco Mattiacci, who lacks experience in Formula One, and Alonso says it is important to allow the new boss time to settle into his role.
"I think we need to give him time and try to see how he settles down," he said.
"It's too early to say if it will be a very good thing or very bad. I think we need to make sure he has all the facilities ready, all the technical stuff ready and all the team behind him to try to help him settle down as fast as possible."