The beleaguered Sunderland boss saw a Jermain Defoe hat-trick steer his side past the League Two battlers but not before a trio of defensive howlers had left the result in doubt
The Grecians twice hit back to reach the break level at 3-3 before Defoe, Jack Rodwell and Duncan Watmore sealed a win which earns Sunderland a home tie against Manchester City.
But Advocaat warned: "I am happy with the six goals but I am totally unhappy with the goals we gave away at this level.
"I don't know if it has to do with concentration or sharpness but they were three crosses and three goals - that's a worry and it's not the first time."
Simon Grayson insisted his Preston side fully deserved their place in the third round after beating 10-man Watford 1-0 at Deepdale through Josh Brownhill's scuffed shot
"No matter who they had out on the pitch tonight they are a Premier League team and have players who have played at the highest level," Grayson said
"We got an early goal to settle us down
We matched them and competed and limited them to few opportunities."
Preston will now face a Bournemouth side who hit four away from home to beat Hartlepool
Teenage striker Joe Dodoo netted a treble while Andrej Kramaric was on target too as Leicester progressed courtesy of a 4-1 win at Bury, for whom Danny Mayor scored
Leicester have been drawn against West Ham in the third round, while Newcastle's reward for a 4-1 win over Northampton is a home tie against Sheffield Wednesday
Carlisle's long trip to QPR resulted in a 2-1 success for the visitors thanks to Jason Kennedy's winner 11 minutes from time after Derek Asamoah and Jay Emmanuel-Thomas traded goals, and the Cumbrians have been rewarded with a tie away to Liverpool
Ricky van Wolfswinkel's first Norwich goal in two years followed Jonny Howson's first-half effort, before Paul Green pulled one back, as the Canaries saw off Rotherham 2-1 to book a meeting with West Brom, who needed penalties to get past Port Vale
Nathan Dyer, Matt Grimes and Marvin Emnes found the net for Swansea in a 3-0 triumph over York which sets up a home tie against Hull, who beat Rochdale 1-0.
The draw produced two high-profile derbies, with Tottenham and Arsenal paired together as well as Aston Villa and Birmingham
Villa advanced as Scott Sinclair scored a hat-trick in a 5-3 win over a Notts County side who led three times at Villa Park, while Birmingham beat Gillingham 2-0 with a brace from Wes Thomas.
Ross McCormack scored twice as Fulham beat the nine men of Sheffield United 3-0.
Ipswich scored three times in extra-time to beat Doncaster 4-1 and earn a trip to Old Trafford to face Manchester United, while Walsall beat Brighton 2-1 to set up a clash against Chelsea.
Charlton were 4-1 victors over Peterborough - Mikhail Kennedy, Karlan Ahearne-Grant, Ahmed Kashi and Igor Vetokele all scoring for the Addicks - and they will next face Crystal Palace after Alan Pardrew's side also scored three in extra-time to beat Shrewsbury 4-1
Everton will travel to Reading if they win at Barnsley on Wednesday night, while Championship sides Middlesbrough and Wolves were drawn together
Southampton will go to MK Dons, who beat Cardiff 2-1, while Stoke - who needed penalties to beat Luton - will travel to Mark Hughes' former side Fulham
Source : PA
Source: PA