Typically the thermal paste should only be about the size of a grain of rice. I then use a old store card (credit card) to apply it evenly over the CPU then put the cooler on. What makes you think you applied it wrong?
I used the paste the came with my stock cooler and it was pre applied. When I put my cooler down on my CPU I had to lift it up to line it up and it kinda smeared on my CPU and I had to clean the sides s bit. I figured it was not a big deal. Idk if I should buy thermal paste and re do it and use your method.