The Frenchman was a key part of Sunday's 5-1 win over Tottenham, but has refused to comment on whether he will be at the club next season.
West Ham United were beaten by Stoke City on Sunday.
Pellegrini is leaving Manchester City to be replaced by Pep Guardiola.
Spurs blew a golden chance to finally finish above rivals Arsenal.
Both players were left out of Crystal Palace's 4-1 defeat to Southampton on the last day of the season.
Arsenal players also said goodbye to Mikel Arteta.
The winger looked in good form and scored a great goal.
Southampton boss Ronald Koeman has been linked with the Everton managerial job.
Newcastle United have been relegated from the Premier League and will play in the Championship next season.
The Spurs midfielder admits "it hurts a lot" that his side were unable to finish ahead of Arsenal as runners-up.