Parkinson, who parted company with the Addicks in January, reckons Brighton are nailed-on to win the title with the race for second place between Huddersfield, Southampton and Peterborough.
The former Colchester and Hull manager guided Charlton to the play-offs last season and had taken them to fifth spot in League One before he was replaced by Chris Powell.
Parkinson plotted Cherries' downfall at the Valley on the opening day of the season and was complimentary about the Dorset club when he summarised for Sky Sports during their defeat at Colchester in Eddie Howe's last game in charge.
Speaking to the Daily Echo, Parkinson said: Bournemouth have done incredibly well. It can be difficult for teams coming up and they have certainly over-achieved.
They have got to be proud of what they have done so far but Lee Bradbury and Steve Fletcher won't want any plaudits just yet. They will want to make sure they are in the play-offs.
Losing key players during the season makes what they have done all the more remarkable. It is very difficult to replace two goalscorers in any team and the fact they have maintained their form is a credit to them.
It was a great decision by the board to keep the job in-house. The players have come through a lot of adversity and you can tell they have got good spirit. That is going to be crucial for them.
Since Parkinson's departure, Charlton have slipped off the promotion pace. And despite winning four of his first five games in charge, Powell has seen the Addicks manage only two draws from their past nine, including a 1-1 against Southampton in midweek. Now 12th, they are currently 12 points behind sixth-placed Cherries, who have also wobbled after losing their past three.
Everyone has a bad run, said Parkinson. It is important for the Bournemouth supporters to stay upbeat and positive. They have got to make sure they don't start getting too carried away with themselves because the team has done really well.
Charlton are a good side and, although they have had a bad run of late, they should not be underestimated. They will be looking to win their games in hand and get themselves back in contention.
As a manager, you have got to keep doing the right things when you have a blip.
If you are getting any criticism, it is important you don't listen to it. You just need to concentrate on what you need to do to win games.