The Wales captain has missed the last three weeks with a long-standing knee problem since joining the Championship club on a season-loan in August.
"He probably overdid it to make an impression at Man City," said Jones.
"He wanted to impress the manager in pre-season and that is understandable. We've just paid that penalty."
Jones' Premier League promotion favourites have lost their last two fixtures as Cardiff have been without Bellamy, fellow striker Michael Chopra and on-loan midfield duo Seyi Olofinjana and Danny Drinkwater.
Bellamy and Olofinjana, who has been struggling with a thigh problem, will have late fitness tests ahead of Cardiff's Championship clash with Millwall on Saturday.
But Jones hopes to have Chopra (ankle) and Drinkwater (thigh) back after the next international break when Cardiff travel to Bristol City on 16 October.
Bellamy has a history of serious knee injuries and has undergone knee reconstruction and career-saving surgery from renowned American knee specialist Dr Richard Steadman.
Steadman gives his patients a thorough rehabilitation and knee-management schedule to ensure career longevity for the athletes that he has treated at his Colorado practice.
The 31-year-old managed his knee problems so well that last season he enjoyed one of his best campaigns, helping inspire Manchester City to fifth in the Premier League and featuring in more than 40 games for both club and country.
But Bellamy publicly fell out of favour with Eastlands boss Mancini over the summer - and despite trying to impress at the big-spending club, he was omitted from their 25-man Premier League squad and left for home-town club Cardiff on a season-long loan in August.
The Wales striker scored one and set up two on his Cardiff debut against Doncaster before starring in a 2-0 win at Portsmouth and playing for Wales in their opening Euro 2012 qualifying defeat in Montenegro.
But Bellamy has been sidelined since with knee trouble and Jones insists Cardiff are "paying the penalty" for his pre-season over-exuberance.
"He did two sessions a day in the summer and with his knee he couldn't do that," said Jones.
"He wanted to show the manager he was ready. He has a programme and he has to adhere to that and that is what got him playing 30-odd games last season.
"I've already said he shouldn't have gone away with Wales in Montenegro but that really wasn't the full cause.
"Maybe he wanted to make an impression at Man City.
"That is why we must play it right. If we don't do it right this time maybe he may have more trouble in three or four weeks time.
"With Craig it is about good injury-management around his playing and training. He has a lot of injuries and enough experience to know how to manage his problems.
"But perhaps he was so eager to impress Man City, he forgot what had previously got him through the full season.
"All Players want to play every game but you must be sensible. Craig, though, is not that far away."
Chopra and Drinkwater are returning to fitness but Jones hopes to have Nigerian international Olofinjana, who is on loan from Hull City, in Saturday's noon showdown with fellow Championship high-fliers Millwall.
"It is frustrating but the main thing is we don't lose them for longer," said Jones.
"The easy option is to throw them all in if they're not fully fit. But we would pay the penalty further down the line.
"It is early in the season so it makes the decision that little bit easier. If it was coming to the end of the season and there was a lot at stake, then I might be forced into doing something I may not want to do and I know isn't right.
"So we will bide our time and we must be patient as they're not far off."
Source: BBC Sport
Source: BBC Sport