The Spaniard said his third place in China, the fourth race of the year, was a confidence boost for Formula One's most glamorous team after a difficult start to the season led to Domenicali's resignation last week.
"I think this podium should be dedicated to Stefano, as everything we do up to July will also be the result of his efforts," said Alonso.
"We have definitely made a step forward, because compared to two weeks ago, we have partly closed the gap to the leaders, but we are well aware there's still a long way to go and we have to keep our feet on the ground."
Mercedes have won every race this year, with Lewis Hamilton leading Nico Rosberg in a one-two finish in the last three including China.
Alonso was only ninth and way off the pace in Bahrain two weeks earlier but Ferrari's improved form, with new principal Marco Mattiacci watching from the pit wall, will be good for morale as the team tries to catch up.
"We felt more competitive and now ... being here on the podium is some kind of surprise for us, a nice surprise finally," Alonso said from the podium.
"We didn't have the start of the season that we would like but at the end of the day we're still in the fight."
The double world champion is third in the standings, 38 points adrift of Rosberg.
Ferrari are fourth overall with 52 points, 102 behind Mercedes.
"This weekend we made some progress and in general, the speed of the car has increased, both in the corners and on the straights," said technical head Pat Fry.
"But we have to be realistic about our current potential and continue working, because the gap to Mercedes is still big and no one within our team has any intention of giving up."
(Writing by Alan Baldwin in London, editing by Pritha Sarkar)
