Nacional, one of Uruguay's "Big Two" clubs with arch-rivals Penarol, sacked Luis Gonzalez after Sunday's 4-1 defeat by Cerro left them in ninth place with nine points from seven matches.
"(Thank you to) those who like me (and) also those who don't because we're all going to be in this together," Carrasco told reporters. "We have all the strength to take on this challenge which is complex but which we're qualified to turn around and leave Nacional at the top.
Carrasco, a former Nacional player is strongly identified with the club and wore their white shirt at his media conference.
"I promise work, seriousness, professionalism and what everyone already knows which is an ambitious footballing idea looking to win and score goals," said the former attacking midfielder.
Gonzalez, appointed in July during the off-season, lasted seven matches including two wins and two defeats. Nacional are five points behind joint leaders Penarol, Wanderers and El Tanque Sisley.
Nacional, 42 times Uruguayan title winners, have been crowned South American and world club champions three times in 1971, 1980 and 1988.
Carrasco, 54, was in charge of the Uruguay team between 2003 and 2004, playing an attractive attacking game that delighted fans but often with serious defensive frailties.
He lost the Uruguay the job after a 3-0 home defeat by Venezuela, traditionally the weakest of the 10 nations in South America, in a 2006 World Cup qualifier.
Carrasco, who also played for Argentina's River Plate and Racing Club, last coached Uruguay's River Plate until last season, steering them to the 2007/08 championship finals.
