Due to his imposing physique, as well as his tenacious style of play, Inter teammate Armando Picchi (who was the captain and sweeper of the side) gave him the nickname "La Roccia" (The Rock).

After short spells at the Friulian side, and subsequently Juventus (where he won the 1960–61 Serie A title), and Palermo, it was with Internazionale that he found his spiritual home in the 1960s, after being acquired in 1962.

[4][5][6][7] A strong, quick, energetic and versatile defender, he was effective both offensively and defensively, and formed a formidable full-back partnership with Giacinto Facchetti, both with Inter and with the Italy national side.

[4][6][10] In the memorable semi-final match against West Germany, often colloquially known as the "Game of the Century", Burgnich even managed to score a goal, helping his team to overcome the Germans 4–3 following extra time.

[15][16] A strong, large, quick, and energetic player, Burgnich is regarded as one of the greatest Italian defenders of his time; his ability in the air, imposing physique, consistency, and his aggressive yet fair, and efficient playing style earned him the nickname "La Roccia" (The Rock), despite not being particularly tall.

A former offensive, central midfielder, he was a tactically versatile, intelligent, and hard-working footballer who was adept at aiding his team both offensively and defensively; he was capable of playing in several defensive positions, and throughout his career, he was deployed as a man-marking centre-back (or "stopper"), as a sweeper (in particular in his later career), and in particular as a right-sided full-back or wing-back, where he particularly excelled in Herrera's catenaccio system, due to his pace, stamina, physicality, and tenacity.

He formed an important partnership with the more offensive minded left-back Facchetti during his career, which is regarded as one of the greatest full-back pairings in football history; although he was less adept at starting attacking plays from the back-line than Facchetti, and initially less likely to push forward during his time at Inter, the more defensive minded Burgnich was an "old-fashioned defender", being an excellent man-marker and a hard tackler, who was difficult to beat in one on one situations.