The Scot, who marks 12 months since he began his second spell at the club on Sunday, oversaw a 5-1 FA Cup third-round victory over League One Oldham on Friday night.
Off-field events overshadowed what should have been a memorable night, with the club and police launching investigations after visiting defender Tom Adeyemi was targeted by abuse from the crowd, but overall Dalglish has been delighted with his first year.
"I've enjoyed the year. It has been fantastic for me," said the Reds boss.
"I think I am fortunate to be here and I have really enjoyed the first year.
"The owners (America-based Fenway Sports Group) have been fantastically supportive and obviously people can judge for themselves whether there has been progress.
"It would be remiss of me not to go on record and show my appreciation for the work (of coaches) Stevie Clarke, Kevin Keen and Sammy Lee - who has now left the club - have done.
"Damien Comolli (director of football) has done a fantastic job in the background on the administrative part of things organising players for us to look at."
Dalglish's first match in charge a year ago ended in a 1-0 third-round defeat at arch-rivals Manchester United - just over 24 hours after having been recalled from a holiday in the Persian Gulf to take over from Roy Hodgson.
Progression on Friday night was only very briefly in doubt when Robbie Simpson, on loan from Huddersfield, smashed in a brilliant 30-yard half-volley but within two minutes Liverpool equalised when Jonjo Shelvey's shot deflected in off Craig Bellamy.
Captain Steven Gerrard, on his first start for two months converted a penalty just before half-time, and after the break Shelvey scored his first goal for the club before late strikes from substitutes Andy Carroll and Stewart Downing - also his first since a summer move from Aston Villa - wrapped up victory.
"It was a better result than the last FA Cup tie," joked Dalglish.
Former Liverpool striker John Aldridge, signed by Dalglish in 1987 in his first successful spell at Anfield, believes the most important thing the Scot has achieved is to restore the club's footballing values.
"He has got us playing football. It is a lot better and there is now a feelgood factor," Aldridge told Press Association Sport.
"With all due respect we weren't playing good football because I think the players lost a bit of belief in Roy and themselves.
"Kenny just grabbed it by the scruff of the neck and got people actually believing in themselves.
"The squad he inherited under-achieved. It wasn't great and should have been doing better than what it was.
"There was a bit of negativity surrounding them but he got them thinking positively straight away and got the ball down and got them playing.
"There has been progression. From where it was this time last year to what I am watching now is a lot better.
"We are not the finished article - we know that and so does Kenny - but at least you can see progression.
"We can get in the top four if we sort our own form out and can win the three big games at Anfield - Chelsea, Arsenal and Tottenham - we have one hell of a chance of doing it."
Oldham manager Paul Dickov took great pride in his side's performance.
"The third goal killed it. At 3-1 we put as many forwards on the pitch to try to get it back and they scored two breakaway goals," said the Scot, who was full of admiration for Simpson's strike.
"Robbie has that in his locker and that was why were so happy to be able to sign him.
"He is a clever footballer and is technical with both feet I think he can play a lot higher than our division.
"There were more positives than negatives from our performance.
"We have another massive game at Huddersfield next week and need to put in a similar performance and go to try to win the game."