So far their only shut-out has come in the 2-0 win against 10-man Arsenal in only the Reds' second match of the campaign.
Even League One strugglers Exeter and npower Championship side Brighton have breached Jose Reina's goal in Carling Cup.
But although lapses at one end have been masked by goals at the other, Dalglish's fifth-placed side currently have a goal difference of zero.
That is worse than eighth-placed Aston Villa and Sunderland, in 14th.
The Liverpool defence is certain to be tested in the 216th Merseyside derby at Goodison Park, and while Dalglish is not overly concerned he accepts there is work to do.
"I wouldn't say we're worried about it," said the Scot, returning to the ground where, just over 20 years ago he quit as Reds boss first time around after an epic 4-4 FA Cup draw citing the pressures of the job for having an effect on his health.
"It's something we've got to continue working on but if we keep scoring more goals than the opposition then fine.
"But it's always nice to have your opposition with a nothing after their name, isn't it?
"Last week against Wolves (a 2-1 win) we might have been under pressure a little bit and got a couple of tackles in around the box but for me we had by far the greater and most chances in the game.
"It looked more likely that we would have extended our lead than lost it.
"If you keep scoring goals, it makes it more difficult for the other team, but certainly losing not goals makes it a bit easier for ourselves as well as scoring at the other end.
"If you want to get points, then it's helpful not to lose any but I wouldn't say we've got a problem with it."
Injuries in defence have not helped consistency with right-backs Martin Kelly and Glen Johnson both missing matches while centre-half Daniel Agger is just returning to training after breaking a rib at Tottenham a fortnight ago.
Kelly is now fit again but neither Johnson nor Agger will be available.
Dalglish made no excuses, though.
"I don't think the changes in defence have affected it particularly," said the 60-year-old.
"Sometimes you go through phases where you don't lose a goal for games.
"We don't like losing goals but we understand in the division we are playing in there are a lot of good teams and good players who are likely to score a goal."
Everton may be below their near-neighbours in the Barclays Premier League, having played one match fewer, and coming off a defeat at Manchester City but Dalglish knows that will make little difference.
"(Everton manager David Moyes) Moysie has done a fantastic job and we've got a great deal of respect for David Moyes and also for the football club," he added.
"They have done well and were unfortunate to have to go to Manchester City last week having played extra time on the previous Wednesday night, not having the benefit City had of making wholesale changes.
"They put on a very resilient performance even though they lost but last year they won 3-0 so we know they will be competitive and we have to match it.
"They will play to their strengths and we will play to our strengths.