Tom Hateley headed home Jamie Murphy's cross after 10 minutes to give the hosts the lead against the run of play.
Motherwell punished Aberdeen's failure to take their chances as Murphy doubled their advantage on the half-hour mark, however Jonny Hayes powered through the midfield before steering an effort past Darren Randolph to reduce the deficit just minutes later.
Murphy notched his 10th goal of the season on the stroke of half-time to provide a timely boost for the Fir Park side and Michael Higdon added a fourth 10 minutes into the second half.
"I didn't feel we were outplayed, Motherwell are probably the best team out with Celtic and we don't like losing to them - and we haven't in the last three times we played them," said Brown.
"All of the credit should go to Motherwell for the way they played. If we don't take the chances we have, then we won't win the match.
"I'm not clutching at straws, I have told the players that it was an unacceptable result and the humility in the dressing room is there to be seen.
"The Christmas message is humility in the performance and determination to banish the disappointment in our next fixture with Dundee."