United fell 12 points behind fourth-placed Arsenal on Tuesday after their 3-0 defeat to Manchester City at Old Trafford.
The fact that one bookmaker is offering 80-1 on United bridging that gap by the end of the season shows just how huge a task Moyes has ahead of him in the remaining seven games.
The Scot is refusing to give up until United are mathematically out of the equation, but Robson does not share the United manager's optimism.
"After losing to Liverpool recently, I think the chance of Champions League qualification has gone," the ex-skipper said in Tuesday's United Review.
Should United not make it into the top four or win the competition - which appears unlikely as they have Bayern Munich in the quarter-finals, it will be the first time the club has not qualified in 19 years.
Indeed United, who are seventh in the Barclays Premier League, have a big task on their hands if they are to make it into the hat for the Europa League.
United are five points behind sixth-placed Tottenham, who have played one more game and sit one point behind Everton, who are serious challengers to Arsenal for the final Champions League spot.
If United end the season seventh, the only way they will qualify for the Europa League is if Arsenal finish fifth and win the FA Cup.
Robson, unlike many, is a fan of the Europa League and he hopes United qualify for Europe's secondary club competition.
"We have to try to make sure we finish above Tottenham Hotspur and Everton in the table," said Robson, who made 461 appearances in 13 years at the club.
"We need that safety net of making sure we finish high enough in the Premier League to qualify for Europe.
"In my opinion, people are wrong to dismiss the Europa League.
"It is more or less a merger of the European Cup Winners' Cup and UEFA Cup and I fondly remember beating Barcelona in the 1991 European Cup Winners' Cup final.
"That was a fantastic night and the memory will never leave me. For me, as a former player, it would be a great achievement to win the Europa League."
Robson, who now works as an ambassador for the club, admits United have been short on self-belief at times this season.
"Confidence is a massive factor in football," he said.
"I know that from my time as a player and I have seen it first hand when I have been a coach.
"When you're down at the bottom, fighting against relegation players lose confidence and it's clearly also hard when they have been so used to success and have found it harder to come by - as has been the case at Manchester United during this Premier League season.
"Some of our displays have lacked the confidence we had become so used to seeing, but it can and will return."