The midfielder started his United career five years before Sir Alex’s appointment, but spent eight seasons under the tutelage of the Glaswegian after he took the helm in 1986.
Sir Alex has won 38 trophies during his 26-year tenure, including 13 Premier League titles, and six major honours during Robson's time at Old Trafford.
"When you think that he's rebuilt probably four or five squads to be successful, and then what he actually did at Aberdeen as well, he's got to go down as the best."
Despite the sudden nature of the announcement, news of Sir Alex’s departure did not come as a surprise after initially deciding to step down in 2002 before performing a U-turn.
"It doesn’t come as a real shock because the boss had considered it before," he added. "I just think with winning the title and getting it back from City this year, I think he maybe thinks, with his grandchildren, that the timing's right."
There is a long-fabled story that Sir Alex was close to being sacked early on in his United career before Mark Robins scored a late winner against Nottingham Forest in the third round of the FA Cup in 1990, with the team going on to lift the trophy that season.
Robson has dismissed the rumours, but feels the impetus drove the club towards their first Premier League triumph just three years later.
"People were speaking about that at the time when we played Nottingham Forest and thankfully Mark Robins scored the goal and we went on to win the FA Cup that year, which gave the players at United a little bit of confidence to go on," Robson added.
"But then the next season, I really do believe that beating Barcelona in the Cup Winners’ Cup final gave the lads the real motivation and confidence to go on and win the title. Thankfully, Sir Matt Busby was still alive at that time because after 26 years, the title was the one that everybody wanted and Sir Alex delivered it. The rest of his success is in the history books."