Carroll scored his first goals for Liverpool following his £35 million move from Newcastle United in January, and for the first time there were signs that his partnership with Suarez could be something for the fans to get excited about.
"You can see the more Andy and Luis play together the better the understanding is,'' said Dalglish. "I thought Luis played outstandingly and was unfortunate not to open the scoring when he hit the post.
"I think everyone can see their partnership is developing but the quality of the service up to them was pretty special last night.
"It is great to see the big man get off the mark. The first one was a fantastic strike, the second a good header.''
Carroll added: "We're just putting a team together now. Me and Luis are new, Flanno (reserve-team defender John Flanagan) played his first game at the back - and I thought he did great - and it shows what we can do for next season.
"The team spirit here is great, there are massive names here, it's a massive club and I don't see why we can't attract big names.
"It was unbelievable. All the lads played well and obviously I got the goals I've been wanting,'' said the 22-year-old of last night's performance. I'm here to score goals, though the result is the most important thing and we got the three points.
"The hat-trick would have been nice but, like I say, the three points is the most important.''
Dalglish also had praise for the young players he had blooded since returning as manager.
Teenage full-back John Flanagan made an impressive debut, having previously been an unused substitute for three Europa League matches. Jay Spearing is starting to develop in central midfield in the absence of Steven Gerrard and Martin Kelly made his breakthrough earlier in the year.
"I wasn't surprised it didn't faze him,'' said the Scot of Flanagan's display. "The development of him over the last year has been fantastic and that is the reward for him.
"Circumstances may have dictated that we pushed him in earlier than we would normally have done but he stood up to it and the good thing for him was he had Jamie Carragher beside him and Dirk Kuyt in front of him.
"The young boy is not bad. For us that is really encouraging as well because it is a reflection of the work that is being done at the academy and if we have a strong academy it can only benefit us in years to come.''
Flanagan said he was surprised to get his call-up in such a big game.
"It was a dream come true. I was told at quarter to six in the team meeting, it came straight out of the blue,'' he said. "But Carra (Carragher) was telling me what to do and keeping my attention focused.''
Midfielder Lucas Leiva also believes the emergence of players like Flanagan points to an optimistic future.
"It was a fantastic achievement not just for him but for the club who are looking to bring young players through,'' said the Brazil international. "Jay is also a very good lad and I think he is doing really well at the moment.
"He's another player coming from the academy and that is what fans want to see. Last night was just one more night when everyone could see Liverpool are going in the right direction and I am happy with the way everything is happening.''
Of the win over City, Dalglish added: "It was very enjoyable. I don't know whether it was the best performance (since his return as manager in January) but it was enjoyable. It was a fantastic performance. I think they thoroughly deserved the 3-0 victory.
"We had plenty of opportunities to add to the three goals and it is a great boost for us beating a team as good as Man City 3-0 and deservedly as well. I don't think it is easy to keep City quiet and I think you should pay credit to them for the way they kept them quiet.
"It was a greater tribute in the second half, even though they were 3-0 up, that they didn't want to lose a goal and they created a lot of chances as well but unfortunately we didn't put any away. It is a great result for the players and won't do them any harm at all.''