Gerrard became the first time a player to score three in a Merseyside league derby since 1982 as his side enjoyed an emphatic 3-0 victory over Everton.
Liverpool, who had lost their last three league matches, remain seventh in the table but move five points ahead of their local rivals whose manager David Moyes endured a miserable evening to mark 10 years in charge of the Goodison Park club.
Dalglish said: "I am not educated enough to add to what anybody else is saying about Steven.
"He has been fantastic for this football club.
"For a guy who left school at 15, my vocabulary is not that great. There is no way I could extol the virtues of Steven Gerrard and do him justice.
"He was fantastic tonight, but I think the three other local lads we had were as well. They didn't do too badly.
"He is the first to say he wouldn't have been there with three goals without the help of the others."
Ian Rush was the last player to score three in the derby while the previous hat-trick in the fixture at Anfield was Fred Howe's in 1935.
Everton boss Moyes made six changes to the team that beat Tottenham at the weekend and the Scot admitted his decision was made with one eye on Saturday's FA Cup tie with Sunderland.
"We have got a big week," he said.
"I am hurt because I am the Everton manager and I have lost to my rivals, Liverpool. I am the same all the time. We will get on with the next game.
"It doesn't make any difference. It is not about me, it is about the Everton players.
"We gave away three terrible goals, all instigated by ourselves.
"The first we were on the break to try to score ourselves, the second we gave away on the halfway line and the third as well.
"We led to our own downfall, but after you give it away you still have to score and Liverpool did that."