An attacking midfielder, he rose through the ranks of River's youth divisions as the team was undergoing its infamous dry spell (18 years, 1957 to 1975, without a championship title).

With reinforcements Roberto Perfumo and Ubaldo Fillol, and the maturing of players like Daniel Passarella, Carlos Morete, J. J. López and Reinaldo Merlo, Alonso led the squad that won both the Metropolitano[9] and the Nacional[10] tournaments of 1975, ushering in a series of seven local titles in the period 1975–1981.

During the 1981 "Nacional" tournament (which River would eventually win), Alonso often clashed with then coach Alfredo Di Stéfano (who seldom selected him for the first team and instead put younger players such as Carlos Daniel Tapia and José María Vieta in his position).

Many talented midfielders emerged from River Plate's youth system during Alonso's reign, including Alejandro Sabella, Néstor Gorosito and Pedro Troglio.

He was also a partner in several commercial ventures, even though he was not an advertising figurehead: his appeal for non-River fans was limited, and Maradona was Argentina's poster boy after his exploits in the 1986 World Cup.