With Saturday's FA Cup final against Chelsea in mind the Scot made nine changes - leaving out the likes of Luis Suarez, Steven Gerrard and Craig Bellamy - but saw his team lose to Martin Skrtel's fifth-minute own goal.
Prior to the match Dalglish had challenged his squad to play for cup final places but admitted after the tally of dropped points at home reached an incredible 30 that he may have made a mistake.
"Their attitude was not right and if you get a bad attitude you are going to get a bad performance and that is what we got," he said.
"I think that is an accurate appraisal.
"I am culpable as well as I changed a lot of players to try to give everyone an opportunity to get in the frame for Saturday.
"I suppose by doing that it was a contributory factor to what happened but you can only be fair.
"I tried to be fair and give everyone an opportunity - maybe I was wrong.
"There were one or two positives but there were too many negatives.
"We cannot play at that tempo, we have to play at a quicker tempo than that. We deserved nothing."
Dalglish insisted that the Fulham defeat will have no bearing on Saturday's FA Cup final against Chelsea.
The Scot had hoped a number of fringe players would stake their claims to be involved at Wembley after making nine changes.
"It will not affect Saturday but that doesn't mean it (the performance) is right and it is not something you want to dismiss easily," said Dalglish.
"It is not correct to go about your work in that way.
"But if we had come in and won 4-0 it wouldn't have made any difference to Saturday.
"There are one or two who did well but apart from that there wasn't anything for us, myself included.
"A lot of people have to take responsibility for it.
"There were some positives. It was nice to see the big lad (Carroll) back.
"He had a niggle at the weekend but he is fit and back and played 90 minutes so that is good for us."
Fulham recorded their first win at Anfield after 30 previous attempts and the only down side was manager Martin Jol was not there to see it as he missed his second successive match with a chest infection.
However, unlike Saturday's woeful 4-0 defeat at Everton, first-team coach Billy McKinlay was expecting an easier phone call to his boss.
"Hopefully I'll have a better conversation with him than I did after the game on Saturday and that performance will cheer him up a bit," he said.
"He was close to coming today [Tuesday] but an extra day or two was needed to shake off this chest infection."
McKinlay said he was not aware of Fulham's previously poor history on Merseyside - they had not won in 48 league visits to the city's two clubs.
"I wasn't aware. I don't worry about history or statistics too much," he added.
"I am delighted. Many things pleased me tonight: the performance, first and foremost, with the result a consequence of that.
"I couldn't be more pleased. Everything which could go wrong went wrong on Saturday but tonight there were lots of pleasing things."
The only goal, ironically, was made by two former Liverpool players with John Arne Riise's cross being deflected on to Skrtel by Alex Kacaniklic, formerly of the youth team.
McKinlay was pleased with the way the team reacted to a 4-0 drubbing across Stanley Park at Everton at the weekend.
"We performed poorly on Saturday but we had a massive response," he said.
"The organisation was better and the players deserve the plaudits."
The win drew the Cottagers level on points with eighth-placed Liverpool and McKinlay believes they should still be aiming higher.
"It is important that we do what we can do," he added.
"We've had a good season. There are times when we think we could have done better and times when we have got away with a result or two.
"With two games to and six points to play for that the target is to push us as high up the league as possible."