That would leave incoming boss Pep Guardiola, who will replace Manuel Pellegrini at the end of the season, with the Europa League to contest in his first year in charge.
Sagna said City should never have been in this position.
"It's very disappointing, especially with the way we started the season," the 33-year-old told British media.
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"But we are to blame. We had everything in our hands to be the best and I believe if we play like we did against Arsenal we are the best team -- but we have to play like this all season.
"To me we deserve to be in the Champions League places," Sagna added. "We can still make it happen. It's vital for us to be part of the Champions League."
City won their first five Premier League fixtures without conceding a goal but saw their title challenge fade with eight wins in 18 games since the start of the year.
They end their season with a trip to Swansea City on Sunday, while Manchester United travel to West Ham for their game in hand later on Tuesday before wrapping up their campaign at home to Bournemouth.
(Reporting by Ian Rodricks in Bengaluru; Editing by Peter Rutherford)
