Manchester - Outgoing Manchester City manager Manuel Pellegrini strived to put on a brave face after his team's chances of Champions League qualification were compromised by a 2-2 draw with Arsenal.
Sunday's result at the Etihad Stadium means that City can only finish in the top four if Manchester United drop points in their two final games or if Arsenal lose at home to bottom club Aston Villa on the final day.
Dropping down to the Europa League would represent a wretched legacy for Pellegrini, who led City to the Champions League semi-finals for the first time this season, but with United facing a testing trip to West Ham United on Tuesday, he said it was important not to abandon hope.
"We have not finished the season," he said. "Of course if you don't depend just on what you can do it is more difficult, but we will see after Tuesday what will happen between Manchester United and West Ham.
"I think we deserve to be in the Champions League next year because we have had 37 games in the spot of Champions (League), so I hope that we are not going to lose that spot in the last game."
Pellegrini gives way to Pep Guardiola at the season's end and his 57th and final home league game was to prove a dispiriting affair.
City led twice, through Sergio Aguero's eight-minute opener and a classy 51st-minute Kevin De Bruyne strike, only for Arsenal to reply on each occasion through Olivier Giroud's header and Alexis Sanchez's crisp finish.
The stadium was half-empty by the time Pellegrini took to the pitch to deliver a short farewell speech.
It was an underwhelming send-off for an understated man who has brought a Premier League title and two League Cups to the Etihad Stadium, but he refused to blame the supporters who left early.
"I was disappointed not to win the game," said the 62-year-old Chilean, who succeeded Roberto Mancini in 2013.
"Winning the three points was a very good way to say goodbye. I have had three unforgettable years here that I want to analyse in this moment.
"We can do it next Sunday (at Swansea City). But the best way to finish with our fans is winning this game and we couldn't do it."