Manager Kenny Dalglish insists there will have no problem in keeping a sense of perspective at Liverpool this season.
The Reds recorded an impressive 2-0 win at Arsenal on Sunday - their first away Barclays Premier League win over the Gunners in a decade.
However, the Liverpool manager maintains no-one will get carried away with talk of an Anfield revolution, and said: "Everybody at Liverpool wants to be successful and win as many games as they can."
He added: "The people who own the club, the people who play for it, from our side - and more importantly the people who support us want exactly the same thing.
"A victory always helps your belief, but you have to manage it. If you lose, you are not going to cut your throat and if you are winning, you are not going to take it for granted you are going to do that every week.
"Everybody will enjoy the moment - it is a fantastic result to come to a place of this quality and win 2-0.
"But we will maintain our dignity and respect, and also keep our feet firmly placed on the ground.
"There is a feeling of contentment, the punters are happy, the owners are very supportive and respectful, and that is reflected through the whole club, which is a wee bit less tense than it used to be."
Dalglish added: "Our supporters are one of the most educated that you will come across. They understand what we are trying to do and they will come along with us. They know we won't be carried away - and neither will they."