Everton missed the chance to confirm a place in next season's UEFA Cup when they were beaten 1-0 by Arsenal in the Premier League on Sunday.
Nicklas Bendtner headed the only goal after 77 minutes at the Emirates stadium against a stubborn Everton side who needed just a draw to guarantee finishing fifth.
Defeat meant Everton can be overtaken by Aston Villa if they lose at home to Newcastle United on the final day of the league season next Sunday. Villa need to win at West Ham United to have any chance of overhauling Everton.
Liverpool, knocked out of the Champions League by Chelsea on Wednesday, won their final home Premier League game, Fernando Torres notching his 32nd goal of the season in all competitions to earn a 1-0 victory over Manchester City.
Both matches had a distinct end-of-season feel about them, although Everton had most at stake.
"There is a lot of disappointment not to get the point but the performance was good, the players stuck at it. It is always difficult here because Arsenal have so much possession," Everton manager David Moyes told Everton's web site (www.evertonfc.com).
"We have been fourth or fifth all year and we want to hang on to it."
GREAT RUN
Arsenal, for whom goalkeeper Jens Lehmann was playing his last home game for the club, showed little urgency in the second half before Armand Traore's great run and cross gave Bendtner the chance to power in the winner.
Wenger was full of praise for his side who have not lost at home in any competition all season.
"We have been outstanding all season," he told the BBC. "We were so close to winning the league so that makes the disappointment even bigger. Let's come back next year and do it."
Arsenal, who have 80 points, can still finish second. Chelsea, who have 81, play at Newcastle on Monday knowing defeat would hand the title to Manchester United.
Liverpool are assured of another crack at the Champions League next season as they are definitely fourth, but there was a subdued atmosphere at Anfield after the midweek defeat at Stamford Bridge ended hopes of silverware.
The hosts had several chances to go ahead with Dirk Kuyt being denied by City keeper Joe Hart and hitting the bar with another headed effort.
Elano struck the woodwork for City with a swerving free kick before Torres broke the deadlock just before the hour mark, accelerating into the penalty area and angling a shot past Hart.
"We should have won by more, we had a lot of opportunities," manager Rafael Benitez told Sky Sports.
Asked about Liverpool's failure to mount a lasting challenge for the Premier League this season, the Spaniard said: "In some crucial moments we were close.
"We must do our best in the league, but we are up against the best in Europe with United and Chelsea, then there's Arsenal, so it's not easy to win the league here."
