Veira started his managerial career with San Lorenzo in 1980, he then had a short stint in charge of Vélez Sársfield before joining River Plate in 1985. Veira had a productive time in charge of River Plate, he led them to the 1985-1986 championship. In 1986 he led them to their first ever victory in the Copa Libertadores and the Copa Intercontinental later that year. In 1987 Veira returned to San Lorenzo where he stayed until 1990. He then returned to the club again in 1992, leading them to the 1995 Clausura championship. In 1996 he became the manager of Boca Juniors, staying with the club until 1998 when he took over as the coach of Bolivia. In 2000 he became manager of Club Atlético Lanús and in 2002 he took charge of Newell's Old Boys.After retiring as manager of Quilmes after only one month in charge Veira returned to San Lorenzo for a fourth time in 2004, by the end of this period, he had been manager of San Lorenzo for 371 games, making him San Lorenzo's longest serving manager in their history.
In 1987 Veira was accused of raping a 13-year-old boy, Sebastián Candelmo. In 1991 he was found guilty of the offence and sentenced to six years in prison. In 1992 he was given a conditional discharge and returned to work as manager of San Lorenzo. Veira has always maintained his innocence, and claimed that the boy was instructed by his mother to make the allegations for financial gains.
He is famous for having a series of bon mots and a very distinctive sense of humour. Some of his classic phrases are:
"¿Qué me parece el hotel?... Un poco antiguo... yo creo que acá mataron a Drácula, nene" ("What do I think about the hotel?...It's a little old... I think Dracula was killed here")
" Pusimos un micro en el arco y la metieron por la ventanilla" ("We put a bus in the goal but they put the ball through the window")
"¿Viste qué calor estuvo haciendo en Buenos Aires? Terrible, hasta Tarzán se insoló..." ("Have you felt the heat in Buenos Aires? Terrible, even Tarzan got heatstroke")
"Pibe, yo tengo un laburo más difícil que el plomero del Titanic" ("Kid, my job is harder than that of the Titanic's plumber")
"¿Viste lo que es ese pibe? Va, viene... va, viene... parece una autopista" ("Did you see that kid? He goes, he comes, he goes, he comes... he looks like a highway")
"¡Pibe! vos no podés ir al ataque ni con ametralladora" (Kid! You can't go in attack even with a machine gun!)
"¡Es una cosa de locos!" ("It's a madmen thing!")
"Me gusta tanto la noche que al día le pondría un toldo" ("I enjoy the night so much that I would pull a blind on the day")
"Para mí el fútbol es... BELLEEEEZZZA" ("To me football is... Beeeeauuuuty")
"Iván de Pineda es una torrrrmenta de facha" ("Iván De Pineda is a cool look storrrrm")
"Qué dupla esa, este (Ruggeri) y el 'Tano' Gutiérrez, ay mamita, criminal , criminal... era Vietnam"
"¡Estos pibes tiran paredes en un campo minado!" ("These kids make wall passes even on a minefield!")
"Esta zona de la cancha de San Lorenzo es terrible, acá lo asaltaron a Rambo" ("This neighbourhood where San Lorenzo stadium is placed, is horrific, Rambo was robbed around here")
"Entiendo la situación del club, pero yo pedí un cuatro y me trajeron un pomelo..."("I understands the club situation, but I asked for a right defender (Cuatro is 4 and also a beverage made of grapefruit) and they brought me a grapefruit").
"La teconologia? Es una cosa de locos. Apretás un botón y estás en la NBA, apretás otro y estás en Moscú" ("Technology? Is a madmen thing, you press a button and you are in the NBA, you press another one and you are in Moscow!!!")