The Blues suffered a disappointing 3-1 loss to bitter rivals Tottenham Hotspur at Stamford Bridge in the Premier League last weekend.
The defending Premier League champions lost to Tottenham for the first time in the Premier League, ending an 18-year unbeaten run.
Chelsea FC are in fifth place in the Premier League table and eight points adrift of fourth-placed Tottenham.
Antonio Conte’s men look unlikely to finish in the Premier League’s top four to leave the Blues facing a season without Champions League football.
The west London side can still finish the season with some silverware if Chelsea FC beat Southampton in the FA Cup semi-final.
Bitter rivals Manchester United or Tottenham will be waiting in the FA Cup final should Conte’s men get past the Saints.
Former Blues winger Nevin has challenged the title holders to end their season with nine successive victories in both competitions.
“Trying to win our remaining seven league games and also the FA Cup must be the main target, but it looks like qualification for the Europa League is most likely now,” Nevin told Chelsea FC’s website.
“In times gone by that would have been considered a pretty damn good season for the club, but much less so in the Roman era I think we would all agree.
“Just considering the dip in finances alone from the lack of Champions League football is enough to blacken the clouds above our heads even more, but it should as always be kept in context.”
Chelsea FC won the Premier League title with two games to spare last season following Conte’s appointment as Guus Hiddink’s permanent successor.
The west London outfit lost 2-1 to Arsenal in the FA Cup final at Wembley last term to miss out on the double following their title success.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news