The Toffees ended the campaign with a 3-1 defeat at West Ham United, but their head coach was adamant that their final league position is an achievement considering that the club was near the foot of the table when he took charge.
"The players picked up the mantle immediately and started to say 'we need to get Everton out of the position we're in'," BBC Sport quotes the former England boss as saying.
"I think you're there to guide them tactically and make them as fit as they possibly can be and try to give them the right direction.
"The players' efforts from day one to now have been very good and we've been sitting in the top half for many weeks now.
"At one stage we looked like pushing Burnley. Eighth is a good finish from where we were at the beginning."
Everton's final-day defeat will likely increase the pressure on Allardyce, who has been strongly linked with the Goodison Park exit this summer.