"I must remind you that Netherlands had a side everyone said was the best for years and they never won a trophy," said Drogba, sitting alongside Yaya Toure and coach Sabri Lamouchi during a rousing airport welcome in South Africa on Wednesday.
The Dutch, who have boasted some of the world's best players for decades, reached three World Cup finals in 1974, 1978 and 2010 without winning one and their only major international title was the 1988 European Championship.
Ivory Coast have twice been African Nations Cup runners-up over the last four tournaments, were semi-finalists in 2008 and in 2010 they were knocked out in the last eight despite leading two minutes from time.
They are top seeds in Group D and play Togo in their opening match on Tuesday and captain Drogba, in probably his last appearance at the tournament, said his nation's time would come.
"We will win it one day, maybe with or without me," said the 34-year-old striker.
"But even if I don't win it, I'll still be part of the team because I have helped to build it over the last 10 years. If not me, or Yaya, then perhaps (Abdul) Razak (of Manchester City), who is the youngest member of the squad."
African Footballer of the Year Toure said the Ivorians would be looking to use the favourites tag in a positive way rather than not fulfilling expectations as in previous years.
"It's true that we are the favorite team and when you have that status you have to take advantage of the quality and experience that you have in our team," said the midfielder, a team mate of 20-year-old Razak's at City.
"We know we have to do better than last year when we lost the final to a better Zambia team. We have almost the same team back again, so it's matter of focus and determination."