Speaking at Ferrari's annual 'Wrooom!' winter retreat in the Italian Dolomites on Wednesday, Domenicali admitted the results they achieved in 2011 were more down to Alonso than the marque's F150° Italia chassis.
Ferrari never recovered from a disappointing start to the season, with Alonso achieving their only victory in the British Grand Prix at Silverstone.
"You always expect more and more from everyone, but to be realistic expecting more from Fernando than what he did last year is difficult," Domenicali said.
"If he can perform at that level again it would be fantastic. But it has to come from our side and the engineering to make sure we're ahead of the others."
He added: "(Alonso) really pushed himself over the limit last year. Over the last two years he's spent more time at Maranello than anyone else in my 20 years with Ferrari. That shows how much it means to him."
Ferrari are currently putting the finishing touches to their 2012 chassis, which Domenicali confirmed would be launched at their Maranello base on February 3.
Although F1's technical rules are currently fairly static - a ban on the use of blown diffusers being the main change ahead of the coming season - Domenicali promised a very different car.
"It's a break with the past, with new concepts never used in a previous car," he said. "The exhaust system is the biggest change and we've been working hard in the wind tunnel to get some extra performance in that area.
"But like last year we will only see the real scenario during qualifying in Melbourne not before because in testing everyone will try to mask themselves."
Ferrari's problems last year, which stemmed from a calibration error in their wind tunnel, led to a shake-up on their technical team mid-season.
Technical director Aldo Costa was replaced by ex-McLaren employee Pat Fry, whose input Domenicali expects will shape performance this year.
"As we say in Italy, he's on his horse now and trying to steer all the people in the technical department in his direction," he said.
"His roots are more connected to the track environment, so it was good to have that input in the technical office. We've relied on him to re-organise the structure the way he wanted to, but it's not completed yet."
Ferrari also struggled generating heat in their Pirelli tyres last year, with Domenicali announcing that former Bridgestone engineer Hirohide Hamashima has been hired as tyre director.
Furthermore, another former McLaren man, Steve Clark, has been appointed to direct trackside engineering.
Ferrari are also busy on the development of a 1.6-litre turbocharged V6 engine to replace the existing 2.4-litre V8s when major rule changes come into effect in 2014.
"We're hoping to fire up the new engine before summertime," Domenicali said. "Having two big projects simultaneously makes these two years very tough compared to other teams that just order engines."
As for Ferrari's other driver Felipe Massa, Domenicali said they would support the Brazilian as he seeks to earn himself a new contract this year.
"He knows this is a crucial season for him and his future and we will do everything for him as a team that we can," he added. "I expect a great season from him."