The Scot admits he doesn't want to put a "dampener" on the club's success, but points out there is considerable time left in the Premier League and his side must be realistic
Liverpool required penalties to secure their first trophy since 2006, after the Championship side were able to end the match with the scores levelled at 2-2.
Despite the victory, Dalglish isn’t keen on dwelling on their success, pointing out they still have to finish the league season strongly in order make sure the club has moved in an upward direction.
Speaking to the club’s official website, Dalglish said: "We should enjoy what we've done but know that we've got to look forward.
"Everybody loved it [the victory at Wembley] but when you like something and you've enjoyed the taste it makes you that little bit more anxious to get back there.
"But we've got a long way to go this season. I'm not trying to put a dampener on anything from Sunday but we've got to be realistic.
"I'm sure we'll move onwards and upwards but we won't do that if we think we've arrived anywhere."
Dalglish also went on to praise Liverpool’s American owners, believing they have done a great job to make the transition a good one, while he was also delighted by the efforts of his players, admitting he was saddened to have to leave some of them out.
He continued: "It's difficult to come into a club like this and have a good transition.
"They came into the club at a difficult time and I'm not sure what targets they set other than to take us forward.
"I don't know if it's going forward quicker than they imagined but they were delighted and we were delighted for them, because they've done a great deal for this football club in the short time they've been in.
"We've had a few disappointments along the way, and I'm sure there'll be a few more to come, but being in the dressing room on Sunday after the game made it worthwhile for everybody.
Dalglish added: "To get some silverware in their first year, it's great credit to every single one of them, not just the new boys. They've accepted each other and they are a very close-knit bunch of players.
"The disappointing thing is that some of them had to be left out [of the final], but even the ones who were left out were there and felt part of it and really enjoyed the celebrations after it."