The Toffees are in a awful run of form as of late, and with fixtures against Liverpool, Chelsea, Arsenal, Leicester and Manchester City all to come in the next few weeks, many fans had hoped for an easier draw in the cup.
The tie will be the first meeting since the Cottagers triumphed 1-0 at Wembley in May previous year.
Arsenal should have a new permanent manager installed by the time the third round comes around in early January after sacking Unai Emery last week.
For Liverpool fans who want the club to remain focuses on Premier League and Champions League success, facing someone like Everton does seem like an unnecessary fixture to play that could potentially prove hard. However, Jurgen Klopp will still want a good run in the FA Cup and they have a huge Merseyside derby to look forward to with Everton heading to Anfield.
Several Everton fans have expressed their disappointment and frustration on social media after the club were drawn against Liverpool in the FA Cup third round.
Manchester United face tricky trip to Wolves, while Tottenham must travel to Championship side Middlesbrough.