Born in Olivos, Carniglia began his career in the fourth division club Club de Olivos, in 1932. He remained there for one season before joining Club Atlético Tigre, but this was only a stepping stone on his way to completing his childhood dream of playing for Boca Juniors, whom he signed for in 1936. His debut, for Boca, was in a friendly played in Parana and was quite a spectacle. Carniglia had a goal within 3 minutes and a fractured left arm by the fifth minute. Boca went on to win the game 3–0. He was part of the Boca side that won the 1940 Argentine First Division and the Copa Dr. Carlos Ibarguren. 1941 was a turn for the worse in his professional career, in a game against San Lorenzo, Carniglia broke his leg. The recovery took three years which he spent at Chacarita Juniors and Atlas, though he was never be the same player again. He prolonged his career by playing in the French Ligue 1 and Ligue 2 with SC Toulon and OGC Nice. Transitioning into the role of manager with OGC Nice. That is not to say that his final years as a player were entirely fruitless, he won the Ligue 1 title and a Coupe de France in 1952, and the Coupe de France again in 1954, all with Nice.
Managerial career
Following his return to OGC Nice in 1953 Carniglia played two more seasons before retiring as a player and taking over the reins as the new Nice manager, from the British manager George Berry. He had immediate success winning the Ligue 1 title with Nice in his first year. The following season, 1956–57, saw Nice finish 13th in Ligue 1. Carniglia then left to take over the Spanish giants Real Madrid. Nice replaced him with the French coach Jean Luciano. Carniglia was Real Madrid head coach from June 1957 to July 1959 with a two-month stop from February 1959 due to a renal colic. Madrid, at the time, had some of the greatest footballing talent in the world with Alfredo di Stéfano, Francisco Gento, Raymond Kopa and Héctor Rial. These greats were joined in 1957 by José Santamaría and Ferenc Puskás in 1958. Carniglia did not have a high opinion of Puskás when he arrived, as he had not played professionally in over a year and was considerably over weight. Carniglia whipped him into shape with Puskás losing 15 kg before his first La Liga game against Oviedo. Carniglia left Puskás out of the 1959 European cup final, which led to his being sacked by Santiago Bernabéu, the chairman of Real. Carniglia's time with Real was the most fruitful in his management career, winning the European Cup twice, in 1958 with a 3–2 win over A.C. Milan and in 1959 with a 2–0 win over Reims. He also won the La Liga title in 1958. Carniglia had short spells at ACF Fiorentina and A.S. Bari before joining Roma in 1961. With Roma, he won the 1961 Fairs Cup. Following his mid season departure from Roma in 1963, apparently due to arguments with the club directors, he took over at A.C. Milan, the team he had beaten in the 1958 European Cup Final. Milan were the reigning European Cup holders and competed in the Intercontinental Cup. They played the Brazilian side Santos featuring Pelé at the height of his prowess in the final 1963 final. Milan won the opening game 4 – 2 in Milan, Pelé scoring both goals for Santos. Before the second leg rumors began to circulate that the Argentinian referee had been bribed, Milan tried to have match official changed but were barred from doing so. Santos won the second game 4 – 2, without Pelé who was injured. With the two leg final a stalemate, a third decisive play-off game took place in Santos just 48 hours after the second leg. The same match official was used for the playoff game. In the third minute, of the playoff, Giovanni Trapattoni was adjudged to have fouled a player in the box and Santos had a penalty, which they duly converted. Cesare Maldini protested and was sent off. Santos won the fixture 1 – 0. Following his retirement as a coach Carniglia had a spell as General Manager of Boca Juniors with Silvio Marzolini as the coach. He was the first president of FAA, his home country's footballers union.