Substitute Dominic Calvert-Lewin responded in added time at Stamford Bridge - but at a point when Everton's elimination had already effectively been secured.
Conte's side host beleaguered Everton in the Carabao Cup at Stamford Bridge tonight, and Courtois now believes the Blues can get back to top form.
The Blues will discover their quarter-final opponents at 4pm on Thursday, as they search for a sixth League Cup in total, and first since 2015.
Yet Chelsea hung on and with minutes remaining made the game safe through Willian.
Chelsea do lack some depth in certain areas of their squad including the midfield/attacking midfield areas and Musonda, although buried down in the pecking order, does provide cover in a number of positions which is a positive for Antonio Conte.
The former Manchester City shot-stopper had been involved moments before, making a good save before a moment of madness almost cost his side the lead. The Toffees haven't won in their last five all-competition games, including painful losses to Arsenal in the EPL and Lyon in the Europa League, and a shocking home draw to lowly Apollon in the Europa League.
The one Chelsea player who didn't allow his performance to drop in the second period, Willian produced a moment of sheer class to steer his side into the hat for the last eight.