City, who won the last of their two English league titles in 1968, appeared on course for a long-awaited third when they led for a majority of the season, until United surged ahead of them a month ago.
With six matches remaining, United have moved eight points clear of City and are in prime position to clinch the title for the 20th time in their history with a successful defence of their Premier League crown.
When United scored two late goals to beat Blackburn Rovers 2-0 last week, City's destiny was no longer in their hands and the 23-year-old Richards told the Daily Mail he realised then just what had been lost.
"At half-time and at 60 minutes, I thought: 'You never know', but United do always look like they will score," he told the newspaper. "So I knew it was going to come.
"But when they got it and went further clear of us, I actually wanted to cry and I haven't done that or felt like that in years.
"Football is full of emotions. You get angry and happy but I have never wanted to cry before. This time I did as that's how much it means.
"I have been grafting so hard this season, we have played unbelievable football and to see United come like this is horrendous. It kills me."
Although the sides are still to play each other at City on April 30, Richards admits their chances of winning the title are now slight.
The situation could change later on Wednesday when United play at Wigan Athletic and City host West Bromwich Albion, but the champions would need to suffer a major collapse to relinquish the title.
Richards added that City's 6-1 win at Old Trafford in October now seemed like a very long time ago but it could have settled the title race had United been managed by anyone other than Sir Alex Ferguson.
"Fergie has got to be one of the best managers that I've ever come across because, if we had got beaten 6-1 that day, United would have been 20 points clear by now," he added.
He also agrees that United are a very special club.
"They used to have [Wayne] Rooney, [Cristiano] Ronaldo, [Carlos] Tevez and [Dimitar] Berbatov," he said, "It was terrifying.
"Now, if you are talking about really special young players, then they only have Rooney. But as a team they are unbelievable. They know how to win. If we can learn some of what they have, then next season we will be twice the team we are now.
"And then we will take some stopping."
