It is five years and three managers since United last won the title but Robson, 61, reckons Mourinho can seal the deal if he is given time.
After Man City defeated Tottenham Hotspur 3-1 on Saturday, Man United needed a win over West Brom to keep the slim title hopes alive.
By completing the job after 33 games, City have emulated the achievement of United, who secured the crown with the same number of matches to spare in 2001.
United's form, and their second-half display against City in particular, have suggested Mourinho's side is capable of challenging their neighbours at the top of the table next season. United hold the current record Premier League winning margin of 18 points and that could also fall to City.
The Gunners conceded less than a goal a game away from home during their Invincibles season, and this one's a cagey affair with both sides aware of the damage the other can do on the break.
"I had a feeling when I woke up this morning but it's a different experience when you're waiting for a team to lose".
Guardiola was phlegmatic in defeat: all City had to do, he said, was win two of its remaining six games. This isn't about Luke Shaw, this is about Jose Mourinho being a very frustrated and angry person because the players aren't doing what he expects of them and he has very high standards.
After completing a year-long sabbatical, he returned to action by managing Bayern Munich where he won the Bundesliga League Title three times.
"If you ask me about respect, I say it is about honesty", he said.
"He has been able to transfer to the team that hunger and desire to never be satisfied".
Pep Guardiola spent the day golfing.
City's title is the 24th trophy of his glittering career.
After the final whistle, the United manager criticised his players. "I want to bring a family atmosphere to the club".