The referee was left in no doubt about sending the Reds defender off, and he will now miss the first three games of next season.
Chadwick should have had two more goals in addition to substitute Craig Garside's fifth for Everton, but the home side were well worthy of their 5-1 scoreline.
They now wrap up the season on Monday at home against Birmingham City and will be in confident mood.
EVERTON RES: Simonsen, O'Hanlon, B Moogan, Clarke, Pilkington, Linderoth, Schumacher, Osman (Garside 77), Chadwick (Barry 81), Symes, A Moogan. Subs: Turner, Beck, Gerrard.
LIVERPOOL RES: Luzi, Vaughan, Wright, Foley, Otsemobor, Babbel, Wilkie (O'Donnell 68),Welsh, Mellor (Flynn 58), Gillespie, Butler (Harrison 60). Subs: Massie.