Alonso goes into the final grand prix of the year in Brazil trailing Sebastian Vettel by 13 points, and with the odds long on overhauling the Red Bull star at the death.
Ferrari's Achilles heel is their one-lap pace on a Saturday as the 31-year-old has qualified on the top two rows of the grid only once in the last nine races since claiming back-to-back pole positions at Silverstone and Hockenheim.
Despite that, Alonso has managed to conjure some astonishing results as he has been on the podium in six of the last seven races to keep his championship hopes alive and take the battle down to the wire.
But if Alonso is to pip Vettel in becoming the ninth driver to win three world titles, he will almost certainly have to at least get ahead of the German on the grid at Interlagos.
"We always say it, but we need to improve our qualifying pace," said Domenicali, in light of Alonso qualifying a dismal ninth in Sunday's United States Grand Prix at the Circuit of The Americas.
"Unfortunately, in Austin we had one of the worst qualifyings of our championship.
"So we need to make sure in Brazil it is a different situation and it doesn't happen again otherwise it will be very, very difficult."
Arguably, Alonso's best hope of victory will be for Vettel to suffer a reliability issue that either compromises his grid position or affects him in the race.
"Pragmatically speaking we know the result has to be better," added Domenicali.
"We have to be in front of Sebastian and we need some drivers in the middle, without thinking of the worst-case scenario.
"This is the approach we need. We know it's not easy because he (Vettel) is driving very well and he has a very quick car.
"But that doesn't change what we have to do. We have to focus on our job and see what will be the outcome of the race.
"But we saw Mark [Webber] had a reliability issue (alternator failure in Austin) and that can happen every time.
"However, I want to stay concentrated on the job we have to do, and prepare the car in the best way we can."
Following the inaugural race at the Texas capital there was a clear sense within Red Bull they had only done half a job after clinching their third consecutive constructors' crown.
As far as team principal Christian Horner is concerned, there will be no let-up or thoughts of playing it conservatively in Sao Paulo.
"We have to approach this race as we have the previous 19," assessed Horner.
"We have to go there, attack the weekend, and get the best out of ourselves, the car, the strategy, the drivers and reliability.
"Anything can happen, as we have seen this season. But it is good to be going there with a lead, and we go there determined to close the job off because we're only halfway there."
Should Vettel duly follow his team's lead and make it three titles in a row, it will be an astonishing achievement for all inside Red Bull.
Horner, however, always suspected the fight for the drivers' crown would not be resolved until the final race of the season.
"We closed out one championship on Sunday," added Horner. "To have won three consecutive constructors' titles is something we could only have dreamed about a few years ago.
"To have achieved what we have over the past three years, in only our eighth year in the sport, is something quite remarkable.
"It is testimony to the long hours, the dedication and determination there is within the team that we've managed to achieve this.
"It is something every member of the team is fiercely proud of, but now we head to Brazil with a 13-point lead, with everything still to play for.
"I've said all season this championship would go to Brazil, and unfortunately I've been proved right."