Sherwood was appointed as the new manager of the Midlands club on Saturday following the sacking of Paul Lambert in midweek and watched the game from the directors’ box before going into the Villa dressing room at half-time when the game was goalless.
Two second half goals from Leandro Bacuna and Scott Sinclair then ensured that Villa’s name would appear in the draw for the next round.
“The boys took his points on board and delivered it in the second half,” Villa caretaker boss Scott Marshall said.
“I think he will have seen the spirit in the dressing room, and hopefully that will continue into the league over the next few weeks.”
Sherwood’s will take charge for the first time next Saturday against Stoke in the Premier League.
The victory against Leicester was Villa’s third in 2015, although they have all come in the FA Cup.
Villa are languishing in 18th place in the league with 22 points from 25 games, having scored just 12 goals all season – the lowest tally in Premier League history at that stage.