Leon Osman's debut goal within two minutes of his full debut at Wolves isn't enough to give the Blues only their second away win of the season, as they go down 1-2 against the relegation candidates.
However, Bolton's 4-1 mauling of Leeds grants the Blues another campaign in the top-flight with just two games to go.
Everton's new kit is unveiled and it is given its first airing in the game against Sam Allardyce's side at Goodison. However, it is an unhappy bow for the new design as Youri Djorkaeff's double helps the Trotters to a 1-2 victory.
Moyes reveals that David Unsworth and Tomasz Radzinski have been offered two-year deals at Everton - but both are still to sign. Meanwhile, reports suggest that the manager himself may also be offered a four-year extension.
In the last game of the season, at Manchester City, the Blues need a point to avoid finishing fourth from bottom with their lowest points total in 24 years. They lose 1-5. Moyes promises change.
"There are no words for that, it just wasn't acceptable for Everton Football Club and it hasn't been acceptable all season and now we have to do something about it," he said.
"We need a drastic change around. There are quite a lot of players we are releasing in the summer, somewhere in double figures, so we will need numbers for the squad if nothing else."
Moyes rejects a £900,000 offer from Fulham for Tomasz Radzinski, while Francis Jeffers is returned to Arsenal after failing to impress during his season-long loan. However, there is good news for Wayne Rooney, who is named in England's EURO 2004 squad.
The Blues bid £7m for Alan Smith, who joins Manchester United, Paul Dickov opts to join Blackburn before Everton and CEO Michael Dunford ends a nine-year spell at the club, with Trevor Birch named as his replacement.