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."
Solskjaer's frustrations were added to by his side's failure to turn first-half domination into goals against Villa.
The Bluebirds hit the woodwork through Fraizer Campbell and a deflected Craig Noone strike, and they were ultimately indebted to two superb saves by David Marshall - from Fabien Delph and Andreas Weimann respectively - to preserve a point.
The result does little for the Welsh club's survival prospects and they remain 19th, effectively three points from safety due to their poor goal difference.
Solskjaer said: "We didn't take our chances, did we?
"The performance was fantastic and we created big opportunities
Brad Guzan made a good save from Fraizer, we hit the crossbar.
"There are no complaints but when you are in the situation we are in it is one of those games where you want to be one or two up at least."
Aston Villa boss Paul Lambert was content with a point which moved his side five clear of the drop zone, which is valuable breathing space in a tightly-packed bottom half.
But the Scot felt his side should have taken more from the game given the chances missed by Delph, Weimann, Gabriel Agbonlahor, Leandro Bacuna and Christian Benteke during the final 30 minutes.
"I am frustrated
I thought in the second half we had enough chances to win it and Marshall, who I knew up at Celtic, has kept them in it, he has made two world class saves," he said.
"I thought Leo should have scored, I thought Gaby should have scored and I thought Christian should have had a shot instead of trying to pass it.
"But Cardiff have beaten some really good teams here
Ole has a good side after taking over from Malky and it is a hard place to come, although I still think we should have won the game."
Source : PA
Source: PA