The Merseyside outfit were beaten 1-0 at Old Trafford tonight, but Rodgers was particularly unhappy with the manner in which his side conceded.
"It was a very close game - decided on a corner at the beginning of the half that we're disappointed with. It just drops into the six-yard box and it's very disappointing to say the least," BBC Sport quotes him as saying.
"The players played really well. They had a few days to adapt to a new system. They created some opportunities but couldn't make the final pass count and didn't work the keeper enough.
"I can have no complaints. One lapse of concentration has cost us."
Liverpool visit Sunderland in the Premier League on Sunday.