Chelsea manager Andre Villas-Boas criticised his side after a 2-0 home defeat by Liverpool in the League Cup quarter-finals on Tuesday and warned they must improve if they are not to avoid an early exit in the Champions League. The London side host Spanish club Valencia next week in their final Group E fixture knowing defeat or a draw would knock them out of the competition at the group stage for the first time. "It was not good today," Portuguese Villas-Boas, who replaced Carlo Ancelotti in the Chelsea hot seat in the summer, told reporters. "It's a pity for us because we had a good chance to progress at home but Liverpool were superior today. "In terms of the Champions League it's life or death -- this level won't be good enough. We have to up the tempo and play that game with the ultimate desire." Villas-Boas said the next month would be a crucial period for the club who are currently outside the top four in the Premier League. "We have to do the maximum with our fixtures. December fixtures include Newcastle, Man city and Tottenham but for us to progress we have to make the most of these games in December," he said. "Bearing in mind that we play these top teams it can put our challenge back on track. "At the moment at home we just haven't been good enough. I think we need to get our fans behind us. You know that Stamford Bridge (fans) have become anxious about playing at home. We have two big games at home where we will need our fans behind us." Second-half goals by Maxi Rodriguez and Martin Kelly, both created by Craig Bellamy, made it a good night for Liverpool manager Kenny Dalglish whose side have now won at Chelsea twice in 10 days following a 2-1 league win.