The on-loan Manchester City player, 31, returned from a five-match absence due to long-standing knee problems and scored the Bluebirds' opening goal.
Bellamy was left out by Wales for the Euro 2012 match with Bulgaria on Friday and the Switzerland game on 12 October.
"He wants to play for his country of course he does," Jones said.
"But he's got to be sensible, because what got him playing over 30 games last year with Man City and his national team was that he was managed right.
"We've got him back up to full speed now and he needs that rest now to get over it and make sure that knee doesn't flare up again."
Jones admitted that he only wanted to play Bellamy for "70 or 75 minutes" at Oakwell, but that he needed to utilise the pace of the striker on the pitch after the 82nd-minute dismissal of Darcy Blake.
Asked if Bellamy would have played next weekend for Cardiff if there was no break for international games, Jones replied: "No, he wouldn't have played and he won't play for Wales, it's not right.
"We've just got to make sure that we do look after him. We've got him this far down the line, it'd be crazy now to put him back into that situation."
Wales caretaker-manager Brian Flynn left Wales captain Bellamy out of the first squad he has named since taking over the reins from John Toshack.
Flynn said that the decision was taken in conjunction with Jones and the player.
Ironically the match with Bulgaria will be played at the Bluebirds' Cardiff City Stadium home, as Wales look to get their campaign on track having lost their opening game 1-0 away to Montenegro.
Wales then travel to face Switzerland in Basel on the following Tuesday.
Source: BBC Sport
Source: BBC Sport