The force you used to push the object is a contact force so as soon as the object is out of your hands there is no longer any contact and therefore no push force. In the absence of friction this object would keep on moving at a steady speed because there would be no resultant force on it. In reality the object will slow down because there is a resultant force acting on it the opposite direction to its motion; this is caused by friction between the object and the surface it is on.