The away side raced into a two-goal lead on Wednesday thanks to a marvellous long-range half-volley from Chris Brunt and an own-goal courtesy of Fabian Delph, but Villa were soon back in it as Andreas Weimann pulled one back before Leandro Bacuna equalised.
Delph made amends for his earlier error with a powerful drive not long before the break, but back came Mel’s side as Youssouf Mulumbu slotted away confidently in the 43rd minute.
The second half was a comparatively tame affair as it produced just the solitary goal, but it was enough for Villa to win 4-3 thanks to a Christian Benteke's penalty that left Mel wondering how his side failed to earn even a point.
He said: "The first 15 minutes is good for us but it is incredible to score three goals away and get no points.
"We need to improve, for example the first goal is a mistake and we need to improve.
"I believe our problem in this game was Benteke, not our defence. We worked all week on the direct play of Aston Villa, I think that this has been our problem."
Mel was also disappointed to see striker Nicolas Anelka leave the pitch midway through the first half with a knee injury, conceding that he may need to find a replacement for the Frenchman before the transfer window shuts on Friday.
"He (Anelka) has a lot of stitches in his knee, at the moment he is out of Sunday (against Liverpool)," the Spaniard added. "I don't know (how bad it is), (on Thursday) we will know a lot more.
"We must try to work to solve the problem that the injury, or ban, to Anelka would cause.
"If we have the possibility to sign a player during the transfer window I believe we should do so."
