Murphy said: "No disrespect to the teams we're about to play, but a club with our ambition has got to think about getting maximum points over Christmas.
"There's been a lot of attention this week on what our chairman said about the Champions League. I think the chairman's comments emphasise that although this season we may have to be realistic and accept fourth, we want to be doing even better.
"I think something which may have been overlooked in all the coverage is that all the players want to be in the Champions League as well. Everyone at Liverpool shares the same ambition. The desire to qualify for the Champions League this season is nowhere greater than in the players. We know if we don't finish fourth we've failed the club.
"It wasn't that long ago we were in the last eight of the Champions League and pushing Arsenal all the way for the title. That's where we want to be again, but we want to be going that bit further."
The Reds midfielder knows the visit of a bouyant Southampton side to Anfield will not be an easy task, and says Liverpool will need to be at their best to take three points.
"Southampton are a very underrated side," added Murphy.
"I watched them beat Manchester United earlier in the season and their work ethic was unbelievable.
"It's the kind of game where we can't be complacent. And we won't be."