1080p just doesn't scale well on 1440p because they don't multiply evenly. If you had a 720p source, it could be doubled to 1440p and look good. And 1080p doubles to 2160 (as in 3840x2160- aka 4K) I know because I have 1440p and have already researched this. You cannot upscale to 1440p from 1080p. Even if you upscaled from 1080p to 2160p, then downscaled it to 1440p (which I don't think is possible), all the resizing would be as detrimental to the picture quality as doing nothing at all.
You may want to dig into the video settings of your media player to see if there are any options to smooth the picture out. Also, make sure you don't have the sharpness turned up more than a little over the default setting, or things can look bad...