PNGs compression causes no quality loss on the image, JPG compression does.
And if you want to get the iamge better looking, do not add it to the already animated image, but create a new one. The gif is limited to 256 colors only and your already indexed image did not have enough different colors for the new frame, so it looked so bad. After you create a new image, the color palette for it will be different. (balanced better)