Sa Pinto agreed a 15-month contract with Red Star, who parted company with Jankovic by mutual consent on Monday after Sunday's 2-1 defeat at Radnicki Nis left them 11 points behind champions and league leaders Partizan Belgrade.
"Red Star is a big club always aiming for titles and we have to try to win the title this season although we know it's going to be tough and the outcome is not in our hands," the 40-year-old coach said.
"I come from Sporting Lisbon, another big club where pressure goes with the territory whether you are a coach or a player, so I am looking forward to the challenge," he said.
Second-placed Red Star last won the title in 2007 and are staring at a trophyless season after they were also knocked out of the Serbian Cup and eliminated from the Europa League preliminary rounds in September.
They also owe in excess of 50 million euros to various creditors and have been unable to pay players' wages on a regular basis this season but club officials said they would find donors for Sa Pinto's reported annual salary of 200,000 euros.
"The money for his income will have to come from outside the club's thin budget and senior managing board members have apparently found creditors," Red Star's sports director Zoran Stojadinovic said.
"Sa Pinto was an outstanding player and I think he has the confidence to become an excellent coach. We don't expect to win the league title this year because that would put him in an awkward position."
Sa Pinto, who was briefly in charge at Sporting Lisbon last year after working as an assistant at Uniao Leiria, played nine years in two spells at Sporting before ending his career at Belgian side Standard Liege in 2007.
He won one league title and two Portuguese Cups with Sporting and scored nine goals in 45 international appearances for Portugal.