Rooney's name was jeered by sections of the crowd when it was announced at Wembley for the World Cup qualifier, and further boos rang out when he scuffed a long-range effort well wide late on during Saturday's 2-0 win.
The 30-year-old was subsequently dropped for the goalless draw in Slovenia, having also been sidelined by Jose Mourinho in recent weeks at Old Trafford.
However, former United skipper Robson expects Rooney to be well received by Red Devils fans if he features in their Premier League clash with rivals Liverpool on Monday, and believes England's all-time leading scorer should be shown more respect by the country's supporters.
"At least United fans will show him the love and respect he deserves," Robson told The Sun.
"Wayne's always given everything for England - just as he has always done for United - and that should always be appreciated.
"He doesn't deserve to be booed like he was against Malta and one thing I do know is that the United supporters will stick by him
Wayne will know that the next time he pulls on a United shirt the fans will be right behind him - as they should be.
"Some England fans seem to forget what he has done for his country for years now. They forget that he is our record scorer, that he is the most-capped outfield player.
"Wayne has done great things for England, no matter that as a country we have not achieved what we would want to.
"Yet whenever he goes through a bad patch some England fans just jump on that bad patch. They don't stand by him. It's not right or fair. He deserves better than what he is getting.
"Most of the England fans are fantastic. They get behind their country, no matter what, and you really have to appreciate that.
"But in the case of Wayne, some of them seem to have a problem. Whenever things go wrong it is always Wayne Rooney's fault - never anybody else's - and that is not right."
Source: PA