David Moyes's Everton visit the red half of the city on Sunday and, after the defeat at Blackpool on Wednesday, the Reds have slipped behind their rivals in the Premier League on goal difference.
Dalglish knows a home defeat would leave them facing the unthinkable - the real prospect of a relegation battle in the coming months.
"It's obviously a big challenge, very seldom do you get a job where you walk in with no challenges," he said.
"The encouraging sign is the attitude and desire of the players, which is quite pleasing.
"The only reason we will have a problem is if they don't show commitment to the club and I think they have shown that - we just need a result.
"There are a couple of things that we can sort out. If the problems lie without yourself you have a chance of solving them and we will work in our own way."