In short, your DM made a bad ruling, and here is why:
(This may seem non-sequitur, but bear with me)
If your DM ruled that "a melee attack" as stated in the Crown of Madness spell description means a full Attack action, then they would also have to accept the same meaning from the following:
Polearm Master: When you take the Attack action with only a glaive,
halberd, or quarterstaff, you can use a bonus action to make a melee
attack with the opposite end.
If you take "a melee attack" to mean a full attack action with the Polearm Master feat, then a level 5 Fighter with an Extra Attack and this feat could, while wielding a glaive, make 4 attacks every round, 2 with your Action and 2 with your Bonus Action, and 6 if they used Action Surge for another full Attack action that round.
The following ability has a similar problem, allowing a creature to take a full Attack action as a reaction if you DM's interpretation of "a melee attack" is applied.
Riposte: When a creature misses you with a melee attack, you can use
your reaction and expend one superiority die to make a melee weapon
attack against the creature.
See also the Monk of the Open Palm's Opportunist ability, and the Against the Tide ability for Hunter Conclave Rangers for similar situations.
Finally, on page 195 of the PHB, Melee Attacks are defined as:
Used in hand-to-hand combat, a melee attack allows you to attack a foe
within your reach. A melee attack typically uses a handheld weapon
such as a sword, a warhammer, or an axe. A typical monster makes a
melee attack when it strikes with its claws, horns, teeth, tentacles,
or other body part. A few spells also involve making a melee attack.
With all this as evidence, it seems apparent that the wording "a melee attack" is intended principally to differentiate it from a ranged attack (which is detailed on the same page in the PHB), but either way, it means a single attempt to hit a target, not a full Attack action.
Also, as a side note, in case anyone was wondering, the phrase "melee weapon attack" as cited in the Riposte text is written that way to show that this combat maneuver can only be performed while wielding a melee weapon, you cannot use the ability if you are unarmed, nor can you use it with a ranged weapon.