LONDON (Reuters) - Chelsea's elimination from the Champions League after losing to Paris St Germain on the away goals rule leaves the English Premier League facing the embarrassing realisation that it is not, as it likes to think, the best league in the world.

A month after clinching a mega TV rights deal, there is a very real possibility that, for the second time in three seasons, no English club will make it into the last eight of European soccer's elite competition.

Arsenal, beaten 3-1 at home by AS Monaco in the first leg of their round of 16 tie, and Manchester City, who lost 1-2 at home to Barcelona in theirs, are both on the brink of elimination ahead of next week's second legs.

Only Everton have reached the last 16 of the Europa League.

Jamie Carragher, who won a Champions League medal with Liverpool in 2005, was scathing in his assessment for Sky about Chelsea's performance, saying that coach Jose Mourinho's negative tactics would never endear him to the wider football public.

"Chelsea are the best team in our league but we are miles away from success. Look at the TV deal that has just gone through," Carragher said.

"We've got the richest league in the world with some of the best players and we want to see the English teams do well, but we are being kidded.

"PSG completely deserved to win it, our teams are miles away. Mourinho could end up the most successful manager ever but his teams will always be unloved because of the way they play."

Gary Neville, who picked up two Champions League medals with Manchester United, and is now working as an analyser for Sky, said: "Chelsea were awful, PSG were wonderful but this result shows you where we are in Europe at the moment.

"Chelsea are out, City and Arsenal are in trouble, Liverpool and Tottenham are out (of the Europa League), we have seen tonight Chelsea, our team best equipped to go on in this competition, have been put out - and deservedly so."