The 56-year-old is planning to climb Mount Kilimanjaro in Africa next month in a bid to help charities including UNICEF, Francis House and cancer treatment centre The Christie Charity, who all benefit from the United Foundation.
Following the Premier League champions' heavy 4-1 defeat to City last Sunday, Robson headed to a bar regularly frequented by fans of the blue half of Manchester.
Despite receiving some jeers, Robson eventually left the bar with £7,000 added to his charity fund.
"I did wonder whether I was doing the right thing going in, but it was worth it in the end," Robson told the Daily Mail. "I took a bit of flak but got talking about what I was doing for United's foundation and these two guys offered to help. Next thing I know one has offered £5,000 and the other £2,000. Incredible."
Former United defender Kevin Moran and 28 others will join Robson on the trek.