Your roster clearly isn't as strong as the top teams so there's really no point in trying to win those games until you upgrade your roster significantly. Losses are losses, the amount you lose by doesn't matter.
If you want to stay in the higher division (you make more $$$ from arena, TV and merchandise in a higher division so personally, I think that's a better move than relegating), just concentrate on winning the games against teams with similar talent. And then play take it easy in the games that you're not going to win anyways. This will make you stronger in the normal games and allow you to play crunch to steal a couple more wins.