The veteran forward missed Tuesday's goalless draw with Aston Villa after club and player "reluctantly" opted not to contest the FA charge for striking Swansea midfielder Jonathan de Guzman with his arm during Saturday's south Wales derby.
Bellamy will also miss the FA Cup clash with holders Wigan and the crucial Premier League meeting with Hull.
The incident was missed by referee Andre Marriner and his team of officials at the time, but it was reviewed by a three-man panel of former elite referees who unanimously agreed it constituted violent conduct.
Meanwhile, Manchester City midfielder Yaya Toure escaped punishment after kicking Norwich striker Ricky van Wolfswinkel at Carrow Road.
Solskjaer believes former Wales' forward Bellamy's reputation has seen him unfairly punished.
"Everyone can see there is a big difference in the decisions (on Bellamy and Toure) one has got three games and one has got away from it," said the Norwegian.
"I don't want to talk about it too much but I think Craig's reputation has gone before him.
"But when you see him in training, even in games he is such a top professional.
"It is a little collision, there is no violence in it, but we just have to accept it, we don't want it dragging on. Craig just wants to stay fit and be ready for the Spurs game.
"We did not feel it was the right decision, I'm sure the referee saw it.
"You look at what they did not give Toure and what they did with Craig and you are not happy with it, you are very disappointed and as I said I think his reputation has gone before him."