The League 2 Choirboys drew 1-1 with the Villans in the original tie ten days ago, earning themselves a trip to Villa Park.
With McCarthy starting at right-back, Wycombe held their own until the final quarter-hour when defender Ciaran Clark headed in a 75th-minute opener for the hosts.
Idrissa Gueye rounded things off in the 90th minute, ending the Choirboys’ challenge and setting up an all-Premier League tie against Manchester City in round four.
In Wycombe’s previous outing, McCarthy and the Chairboys suffered a 1-0 defeat at Hartlepool, as they lost a second successive game in League 2.
Scott Fenwick’s 33rd-minute goal separated the teams, as he converted at the near post after Nathan Thomas had eluded McCarthy out wide and whipped in a wicked, low cross.
McCarthy, playing at right-back, was substituted in the 68th minute for midfielder Jermaine Udumaga, as Wycombe chased an equaliser, but they were unable to find one, as they remained sixth in the table.
In League 1, Jordan Turnbull played the full game for Swindon Town, as they came from 3-1 down at home to beat Crewe.
The Robins led through Nicky Ajose’s early strike, but the visitors equalised after 20 minutes, when Brad Inman latched onto Turnbull’s under-hit header back towards his own keeper.
Shortly afterwards, Ryan Colclough worked space in the box to finish at the near post, and Crewe led 3-1 before the interval when Inman slotted home.
But Town’s stirring fightback began two minutes after half-time, when Jonathan Obika headed in from close range, and the hosts were level in the 52nd minute after Ben Nugent accidentally headed Brandon Ormonde-Ottewill’s cross into his own net.
It looked as if the match would end level, until Ajose popped up in the 90th minute to finish from six yards out, after Crewe keeper Ben Garratt palmed a Yaser Kasim shot into his path. The result moves Town up to 14th in the table.
Elsewhere in League 1, winger Lloyd Isgrove helped Barnsley win a third successive match, as they triumphed 3-0 away to Shrewsbury Town.
Sam Winnall struck twice in the space of six first-half minutes to put the Tykes in a commanding position, and they finished things off in the 72nd minute when Alfie Mawson forced home from close range after a scramble in the box.
Barnsley remain 17th in the table, but are now four points clear of Shrewsbury, who occupy the final relegation spot.