The Reds were forced to come from behind after Nikica Jelavic had capitalised on a Jamie Carragher mistake to give the Toffeemen a half-time advantage.
But an equally disastrous blunder from Sylvain Distin gifted Luis Suarez an equaliser before Andy Carroll silenced the doubters by ramming home the winner three minutes from time.
It means Liverpool will have the chance to add an FA Cup to the Carling Cup they won in February when they face either Chelsea or Tottenham at Wembley on May 5.
However, Dalglish is refusing to get carried away.
"It is called a work in progress," he said.
"We have said that many times before and there is no need for us to change.
"After the Carling Cup I said we are not the finished article and we are saying the same thing now."
Nevertheless, after what Dalglish accepts has been a difficult period, culminating in the departure of director of football Damien Comolli on Thursday, a rather strange season would surely be regarded as a success if Liverpool ended it as a double trophy winner.
"Winning gives you a good feeling," he said.
"If you can't enjoy winning, you might as well put the lid on the box because it is time up.
"Whether it helps or hinders lies with the individual.
"You can get a taste of it, think it is great for us to go forward and try and win something else because you enjoyed that so much or you can go complacent and say that is great we have won a trophy, that is all I wanted to do.
"The most important thing is that the players want to be more successful than they have been."
That Carroll should score the winner was sweeter because the £35million man had wasted a golden chance to equalise at the start of the second half when he nodded Stewart Downing's excellent far-post cross wide from point-blank range.
However, as is his preference, Dalglish spread the praise amongst his entire squad rather than concentrate on the character of one individual, no matter how high profile.
"It is testament to everybody's character," he said.
"They have held themselves together and had the resolve to come back and respond positive to what has not been a great period in the club's history.
"It is not a time for us to sit down and individualise performances and go through everyone who has been on the pitch.
"It is a time for us to enjoy the moment, be respectful to Everton and over the next two or three days get back to work and make sure we are fully focussed on the league games and the cup finals still to come.
"It is not a tap you can turn on and off. If we don't keep going we won't get success."
Opposite number David Moyes could only offer words of sympathy for Distin, who apologised to Everton's supporters after the game.
However, there was no hiding the fact Moyes felt the badly-hit back-pass was the game's turning point.
"Sylvain is really down," said Moyes.
"He has been here a couple of times before and has won the FA Cup before with Portsmouth.
"He knows exactly what it means and how important it is. He has been great for us so far.
"But I said there would be little between the teams. I thought there would be defining moments and they were there for all to see."
It maintained an unhappy sequence of big-game defeats for Everton against their fierce city rivals, which did not make Moyes feel any better about his plight.
"It is not just me who as a manager has had to sit here and do this at Everton," he said.
"There was always a chance that would happen. You are playing against a big football club aren't you?
"But I thought the way we had been playing it was our chance.
"Liverpool have not been where they would like to be and we had been playing well.
"That is why the game was very even and there was very little between the two teams.
"But a couple of small margins changed the result.
"I feel for them all. We are all in it together, whether it is someone who makes a mistake or not. That is the way it is here."