(CNN) -- Manchester United manager David Moyes says he and his slumping team are "desperate" to turn things around -- and hopes the reversal of fortune begins in the Champions League.
The defending Premier League champion didn't lose any ground in the title race -- although repeating was already looking unlikely -- but the Red Devils did slip 12 points behind a Champions League spot after the most recent round of games last weekend.
And United wasn't just beaten on Sunday. It was outclassed by arch-rival Liverpool at Old Trafford, 3-0.
While Liverpool routinely threatened thanks to the likes of in-form pair Luis Suarez and Daniel Sturridge, United's high-profile duo of Wayne Rooney and Robin van Persie were never a problem for the Reds' sometimes shaky defense.
With Liverpool controlling the midfield, United struggled to gain a foothold and managed just one shot on target.
"The players are capable of turning it around," Moyes was quoted as saying by Manchester United's website. "We're all desperate to put things right and make sure we play better to give the supporters here something to shout about."
The manner of the defeat piled more pressure on Moyes, who is in his first season at the helm at Manchester United after replacing managerial great Alex Ferguson.
Former Liverpool defender Alan Hansen said Moyes is "fighting for his future" and that if United exited the Champions League against Olympiacos and then lost to Manchester City in the league, "there will be serious doubts over whether Moyes can continue."
According to British bookmaker William Hill, Moyes is the joint third favorite -- behind West Bromwich Albion's Pepe Mel and Norwich's Chris Hughton -- to become the next Premier League manager to depart. West Bromwich Albion and Norwich are struggling near the relegation zone although West Brom won Saturday at Swansea.
Manchester United faces an uphill battle to reach the last eight of this season's Champions League after a 2-0 reverse in Greece: Only once has the team lost a first leg in the competition and advanced -- in 2006/2007 against Roma.
But Olympiacos has lost all 11 of its previous encounters in England and United has won all of its home games versus Greek opposition.
Given United's position in the Premier League, winning the Champions League might be its most feasible path to appearing in next season's competition. United last failed to compete in the Champions League in 1995/1996.
"We have to go for the throat to get the win," said Moyes. "We won't be gung-ho but we will certainly go with a mindset to overhaul the deficit as quickly as we can.
"We won't be reckless as we could find ourselves with a bigger mountain to climb but we can be forceful. We have to be if we're to keep ourselves in the Champions League."
United midfielder Juan Mata, bought in the January transfer window for a club record $61 million, said United's pedigree in Europe -- it has amassed three titles in Europe's top club competition while Olympiacos has yet to make the semifinals -- could be a factor.
"Everything went bad (against Liverpool)," Mata wrote in his blog. "It was a tough defeat and I want to tell you that we will give everything we have in order to forget about this in the remaining games. And there is a very important one around the corner.
"We know the history of this club and its achievements, based on a winning spirit. That is what we need to beat Olympiacos and get through in the Champions League.
"The storm will pass and the sun will rise again," the cup-tied Spaniard also said. "I have no doubt. Besides, no one said this would be easy."