There is much information to analyze. But I guess:
1. In low levels, deviation of team qualities of all teams is small. I expect that the deviation of qualities of teams in Cup reduce even more.
2. In low levels, there are less aggressive managers who are higher level than you, and will improve their team quality through buying high quality players that you have no way to buy after cup drawings.
3. Maybe relative quality of your team is not too high. Then you do not draw with many higher level teams.