You do have feelings for your ex. You just don't have (or at least don't want to have) actions for her.
The distinction is important – it's okay to be bothered by your feelings, so long as you don't act on them in a fashion that externalizes the negativity, and harms your ex, her new boyfriend, and/or their relationship.
The best solution, hokey as it sounds, is to accept those feelings, really dig into them, and work on figuring them out. Do they disappear when you yourself have a relationship, or even a date? Do they lessen or increase when you remember the good (or the bad) you shared together? Figure it out.
Then, as best you can, work on venting the bothered feeling safely, diffusing it into mere nostalgia, or crystalizing it into a commitment to bettering yourself and your future relationships.
More than anything, it sounds like you need to transition from a mindset in which you've lost something, or failed to keep hold of someone, into a disposition of having successfully completed your relationship. Outlook and attitude count for a lot, and showing that you can embrace and survive failures – rather than mourn or dwell on them – is a highly attractive trait to future potential mates.
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