Kenny Dalglish struggles to handle the good times with Liverpool

Wembley encounters with Everton have a tendency to leave Kenny Dalglish nursing a sore head. He was accidentally nutted by a supporter while resisting attempts to chair him from the field after the 1989 FA Cup final, and left with blood running down his face. On Saturday, it was questions he was running from. Dalglish was cornered in the press theatre and it did not feel much like a victor holding court as he fumbled behind him for the door handle.

This is Dalglish's way, though by the time he had sprung that door and vanished, we had been privy to perhaps the first impression of how much of a struggle his Liverpool salvation mission has lately turned out to be.

"To go forward and be successful, sometimes you need to get battered along the way," he reflected. "It is important for everybody to go through some bad bits to realise how good the good bits are. I have been there before and I suppose I will be there again at some stage."

The manner of Liverpool's progression to the FA Cup final – in which for the most part they were 11 players failing to resemble a team – did not permit Dalglish much enjoyment, even though they held sway enough to make the rather ungracious conclusion of Everton's Tim Cahill that Liverpool "just seem to have luck on their side when they play Everton" an unjustified one.

The winning team's display in an uninspiring match made Cahill's reflection that Liverpool "are going to find it difficult to win the final" a more debatable one, though judging them on performances alone is to overlook that quality which no-one can deny Dalglish delivers: the mental sharpness to get the result on the big occasions.

Liverpool's journeys to two Wembley finals have taken them past both Manchester teams, Chelsea and Stoke City (twice) and when Jamie Carragher had recovered from the calamity of gifting Nikica Jelavic Everton's opener, he observed how there was "something in our DNA" which enables Liverpool to win through in the end.

"I don't know how we do it, but Liverpool have always done it in the past," Carragher continued. "There is something from within which not all clubs have got. Manchester United have got it too: finding a way to win at big moments. I can't put my finger on what it is, but I'm delighted we've got it."

It is a quality which means more to supporters than the modern holy grail of a top-four finish, though perhaps Fenway Sports Group do not share that appreciation. It seemed a miscalculation that both John W Henry and Tom Werner should have missed this occasion to be back in Boston.

With every season without Champions League football widening the chasm between Liverpool and the elite, the Americans may not be encouraged by Carragher's astute observation that the side are not matching their cup success in the Premier League because "with one-off games" it's different. "I don't think we won because of our great ability or great players; it's a character thing," Carragher said. "The teams at the top are the best teams but in one-off games we have something inside us. I don't think anyone could have that on a weekly basis but you can at certain moments."

An FA Cup final probably keeps Dalglish in situ next season but silverware will not always be enough for FSG. Steven Gerrard was also a realist about where the club stands. "I think the proof is out there. We've proved we're a very good cup team but there's still a very big challenge for us in the league," he said. He suggested that complacency had set in after the Carling Cup final victory over Cardiff City in February, though billeting Jordan Henderson, who doesn't cross, and Stewart Downing, who has generally forgotten how to, either side of Andy Carroll suggested that this is actually a story of new pieces failing to fit the puzzle.

The matchwinner Carroll is the most puzzling of all. Just when there are signs that he is delivering, Dalglish consigns him back to the bench. He has never started more than three consecutive games this season. Little wonder that the striker whom Carragher had left behind in the dressing room was not doing cartwheels. "Sometimes the emotions in the dressing room are different to what people expect," Carragher said. "You just sit there quiet."

Carroll is worth persevering with, while Luis Suarez said he wants to hang on. "Yes, yes I will continue at Liverpool. It is obvious. I have four years left on my contract and I am very happy," he said after a big performance.

If Wembley can buy Dalglish enough time, there are players to take Liverpool on in a more substantial way.

Scorers: Liverpool Suarez 62, Carroll 87. Everton Jelavic 24. Subs: Liverpool Rodriguez (Henderson, 75), Bellamy (Downing, 84). Everton Coleman (Gueye, 68), Anichebe (Baines, 88). Booked: Liverpool Skrtel, Henderson. Everton Distin, Jelavic, Coleman.

Man of the match Suarez. Match rating 6/10.

Possession: Liverpool 55% Everton 45%.

Attempts on target: Liverpool 7 Everton 5.

Referee H Webb (S Yorkshire). Attendance 87,231.