Manchester City manager Manuel Pellegrini says it is "a disaster" for big teams to miss out on the top four - unless they win every other trophy.
City were beaten by Real Madrid in the Champions League semi-final on 4 May.
They face Arsenal on Sunday knowing they still have to qualify for next season's competition.
Pellegrini said: "If you are not in the top four it's a disastrous season but if you win the Champions League, FA Cup and League Cup, it's a very good one."
Some of the Premier League's most frequent Champions League qualifiers from the past decade could yet fail to make it into the 2016-17 edition.
Ninth-placed Chelsea, winners in 2012, know they will not finish in the top four.
Liverpool have the slimmest of possibilities to make the top four but could yet qualify for the Champions League as Europa League winners, having made the final in Basel, where they will play Sevilla on 18 May.
One win from the final two games of a season that ends at home to relegated Aston Villa on 15 May will be enough for Arsenal.
It leaves City battling with fifth-placed Manchester United and sixth-placed West Ham, who play each other in the final game at Upton Park on 11 May.
Manchester United will close the gap on City to a single point if they win at Norwich at lunchtime on Saturday. West Ham will be two points behind if they beat Swansea later the same day.
Pellegrini said: "Last year, when we didn't win any titles, it was not a good season but it was not a disaster.
"When you are not involved in the next season's Champions League, that is a disaster for all the big teams."
'For the media, the season finished on 1 February'
Sunday's game will be Pellegrini's last at Etihad Stadium as City boss.
After three seasons in charge, the 62-year-old leaves in the summer, with Pep Guardiola arriving in his place.
When the managerial change was announced on 1 February, City officials felt it would have no impact on the team's performance.
However, from a points average of 1.91 per game, City have slipped to 1.77, winning six of their 13 matches and losing five times in the Premier League.
"For a lot of media this season finished on 1 February when people started talking about next season and who was leaving and who was staying," said Pellegrini.
"The players have had to read that since then and it is not easy."