The Liverpool midfielder was dismissed in the 39th minute after a lunge on the Northern Ireland defender but Rodgers believes Evans was also culpable and should have been punished.
Robin van Persie scored from the penalty spot to secure a 2-1 victory for United after Rafael had cancelled out Steven Gerrard's opening goal.
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"I thought the best team lost. What you can't control is decisions by the referee. The players were outstanding."
The former Swansea City boss also provided a damning verdict on referee Mark Halsey's decision to award a penalty after Antonio Valencia was judged to have been tripped by defender Glen Johnson.
"It was never a penalty," Rodgers claimed. "It was just one of those days. The decisions just didn't go our way. I think we were harshly dealt with today. We'll soon turn these results into wins.
"I think performance wise everybody can see the growth. I'm pretty sure our luck will change and then we'll fly."