Liverpool and Chelsea grabbed the final two Champions League places but Leicester City fell short of a top-four finish for the second successive season on a nerve-jangling final day of the Premier League season on Sunday. Liverpool avoided any drama as they beat Crystal Palace 2-0 to finish in third spot -- a silver lining to a difficult season in which their defence of the title crumbled. read more Chelsea lost 2-1 at Aston Villa -- a result that could have been curtains for them in the top-four battle. read more But they were saved as arch-rivals Tottenham Hotspur twice came from a goal down to win 4-2 at Leicester City. [nL2N2NA0E1} Harry Kane was on target for Tottenham to win the Premier League Golden Boot award for the third time with 23 goals while Gareth Bale struck twice late on. Jamie Vardy scored twice from the spot for Leicester who also let a top-four finish slip last season in the final week. Liverpool finished on 69 points with Chelsea on 67 and Leicester, who will enter the Europa League, on 66. Sergio Aguero came on in the 65th minute and scored twice in his final league game for champions Manchester City as they thrashed Everton 5-0 before being presented with the trophy on the pitch in front of 10,000 fans at The Etihad. {nL2N2NA0ES} Argentine Aguero now has 184 Premier League goals for City, the most of any player for a single club in the competition - one ahead of Wayne Rooney"s tally for Manchester United. City manager Pep Guardiola, who has now won three Premier League titles in his five seasons at te club, broke down in tears as spoke of 32-year-old Aguero"s impact at the club where he has spent a decade and became their all-time leading scorer. "We love him so much, he"s a special person for us," Guardiola, who will lead City out in their first Champions League final when they play Chelsea in Porto next week, said on the pitch. "We cannot replace him." Aguero, who could end up at Barcelona next season after his contract ends next month, will always be remembered and adored by City"s fans for his heart-stopping late goal earned the first of the club"s five Premier League titles in 2012. "Before the game I felt so strange, the sensation is not good. I prefer to think about the good moments," he said. Second-placed Manchester United beat Wolverhampton Wanderers 2-1 to finish 12 points adrift of City. It was Nuno Espirito Santo"s final game as manager of Wolves. HAPPY HAMMERS West Ham United will join Leicester City in the Europa League after finishing sixth - rounding off a superb season in style with a 3-0 home win over Southampton. Tottenham will be England"s representative in the inaugural Europa Conference League although that will be scant consolation for the London club for whom Kane could have possibly played his last game on Sunday, with a big-money move likely. Bale also scored twice for Tottenham on what was probably the last game of his loan spell from Real Madrid. For a long time it had looked as though Liverpool would miss out on the Champions League, but Juergen Klopp"s injury-hit side ended the season with five successive wins. Sadio Mane struck twice against Palace in what was 73-year-old Roy Hodgson"s last game in charge of the south London club. "If you had told me five weeks ago that we would finish third, I would think it is not possible," Klopp said. "I"m so proud of what they"ve done the last 10 or 15 games and the reaction of the team in bad times." Chelsea can now go into next weekend"s Champions League final against Manchester City without the added pressure of needing to win it to be part of next season"s competition. But they hardly helped themselves. Villa led 2-0 with goals by Bertrand Traore and an Anwar El Ghazi penalty before Ben Chilwell pulled a goal back for Thomas Tuchel"s side. It did not matter that they could not equalise as news drifted through of Tottenham"s win at Leicester. "The performance was by far good enough to win the game. We did not score, conceded two cheap goals and it was a defeat in the end. We are lucky to escape today," Tuchel said. Chelsea"s midweek win over Leicester, revenge for their FA Cup final defeat, ultimately proved decisive. "It"s hugely disappointing for us. We fought so hard all season," Foxes boss Brendan Rodgers said. Bottom club Sheffield United bowed out with a 1-0 win over Burnley, while Leeds United claimed an impressive ninth place by beating relegated West Bromwich Albion 3-1. Arsenal finished one position higher with a 2-0 home win over Brighton & Hove Albion.