Making his first return to the Anfield dugout since leaving the club nearly 20 years ago, Dalglish was greeted by banners and cheers and was soon punching the air in celebration when Raul Meireles put Liverpool ahead in the 29th minute.
Any elation was wiped out seconds after the break when Sylvain Distin scored for Everton and Dalglish was left silently shaking his head six minutes later when Jermaine Beckford made it 2-1 as the visitors found an edge missing in the first half.
"We've got to be conscious of the fact that... Jay played really well today and there's Jonjo Shelvey, Daniel Pacheco, Danny Wilson. We've got to be careful that we put them in and don't destroy them," Dalglish told a news conference.
"Equally we've got a couple of senior players who the supporters haven't exactly seen eye-to-eye with and we've got to try to rebuild them because they could be valuable acquisitions for us as well.
"If we can get Christian (Poulsen) and Paul Konchesky back on side then that makes the squad that much deeper."
"There is a lot of belief coming back into the players and that is great," said Dalglish, who did not sit down for the whole of his first home match since taking over last weekend.
"I was disappointed with the first half because I thought we never got to the pitch of the game, I thought we looked as if we had some young players in the team who looked as if they were a little overawed with the start of the game," said Moyes.
"I'm disappointed we didn't take all three points after the second half but delighted we were only 1-0 down at half-time - Liverpool were the better team."
