Sometimes past relationships stay with us for awhile. This can be true regardless of how it ends. Maybe someone was dishonest and it ended immediately, or maybe it "ran its course" and things ended over time. Regardless of how it ended, there are always feelings left, it is just a question of how strong and for how long.
When these feelings are still with you, it is not a sign of weakness. It is a sign that you are able to feel, and you are able to love. Many of us want to "skip" this time by finding someone else relatively quickly, keeping the amount of time we are alone to a minimum. These choices are completely up to the person, but remember that any incompleteness in the past relationship will still need to be worked out. Keeping it inside and finding someone else does not mean you are "over" it, keeping it inside just means the feelings will come out later.
Do the work to be complete on a past relationship. Even if it’s painful, the feelings will always find a way out.