The seven-time world champion, 37, instead insisted that he would figure in the final reckoning and said he also thought at least three other drivers could challenge for honours.
Spaniard Alonso went on to win the title, holding off a strong challenge from McLaren rival Kimi Raikkonen, and in so doing, became the sport’s youngest ever champion.
German Schumacher also hinted that Honda’s Jenson Button of Britain and Brazilian Rubens Barrichello could follow on their winter testing form and compete for the title.
Schumacher said: “I think there’s more than three [championship favourites] because honestly, Honda have their two drivers and also we all have team-mates so it’s going to be a nice season for all of us.”
Ferrari’s own preparations for the season-opening Bahrain Grand Prix have involved an intensive winter of testing, and Schumacher believes the Scuderia will bounce back after a disappointing 2005 season in which he only tasted victory once.
He added: “We have worked very hard and we certainly have improved the game, but then it’s always the question: have we improved enough?
“It’s something we will find out this weekend. As always we have had a long winter, a lot of talk, a lot of question marks and finally we answer them, in a way, at the first race. I think it will be closer this year.”
Schumacher also laughed off suggestions that losing Barrichello to Honda would strongly disadvantage the team and instead said that new team-mate Felipe Massa, also from Brazil, would be a vital member of the Italian team.
When asked if Massa would disadvantage the team, Schumacher replied: “No. First because Felipe is quite experienced. Second, it depends on the team and on how you develop, with the team, a new car.
“The only question we have is in terms of driving style. Maybe we have different driving styles that require two different set-ups so it will be quite interesting to see if I can profit more than I used to or not.”
Ferrari, who will use Bridgestone tyres for the eighth year in a row, were the only one of the Japanese tyre manufacturers’ partner teams to test at the Sakhir circuit over the winter and Schumacher thinks it will be beneficial to him.
He added: “First of all, we did everything to schedule, we did more running than we planned to do.
“It’s true the weather wasn’t great, but for what we had to do we figured out our issues. It’s true as well we would have loved to do more kilometres, but we are more prepared because the car was quick right from the beginning and even quicker now and I think we can be quite confident to be reliable as well.”
For his part, Alonso says he wants nothing less than a repeat of his drivers’ world title but tipped Honda to surprise this year.
Formula One’s youngest champion, 24, who won seven times last season, believes Honda, and drivers Jenson Button and Rubens Barrichello, will be amongst his Renault team’s title challengers, despite having not won a race since John Surtees triumphed in the 1968 Italian Grand Prix.
Alonso said: “I have the number one on my car, so it’s a dream come true, and I think we will start strong, but it will be very difficult to repeat our success from last year. I will try my best though.
“It will be an interesting season I think, we will have competitors for sure; McLaren, Honda, Ferrari, but I think that I will have more confidence now that I have already won one world championship.”