Former Everton manager Howard Kendall believes the Toffees must now target Champions League qualification.
David Moyes' men ended the last campaign with an FA Cup final appearance and a fifth-place finish in the Premier League.
Kendall told BBC Radio Merseyside: "They've achieved so much so far and you have to be ambitious enough to want to go further.
"Fourth and upwards has got to be the aim and a trophy as well."
Kendall, a former Everton player, who is most famous for leading the club to a league championship and European Cup Winners' Cup double in 1985, brims with pride when he reflects on his former side's achievements over the last 12 months.
"I know there's no silverware but they've had a tremendous season to finish where they have in the league, with the injury problems they've had," he added.
"To get to the FA Cup final, although disappointing not to win it - it's been a very, very successful season."
Everton's 2-1 defeat by Chelsea in last month's Cup final stretches their trophyless run to 14 years.
Moyes has previously led Everton into the top four in 2005 and Kendall feels he is the right man to end the Goodison Park trophy drought.
"I'm sure David is as keen as the rest of the fans to bring a trophy to Everton. He'll have been very disappointed last weekend but the future is his," said Kendall.
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