An entertaining clash ended 2-2, with Raul Mereiles opening the scoring before Everton turned the game on its head at the start of the second half, with Sylvain Distin and Jermaine Beckford firing them 2-1 ahead.
Tim Howard brought down Maxi Rodriguez in the area midway through the second half to allow Dirk Kuyt to snatch the Reds a point from the spot.
"I am disappointed we didn't take all three points after the second half but delighted to only come in 1-0 down after the first half because Liverpool were the better team," Moyes said.
"In the first half we never got to the pitch of the game and it looked as if we had some young players in the team who looked overawed by the start of the game.
"Liverpool won all the duels so it needed a word to correct it at half-time and in the second half we were terrific. I thought we had a chance when it went to 2-1 because we were on top but we were missing three or four big players. I know Liverpool were missing two (Steven Gerrard and Jamie Carragher) but it is different for a club like Everton, who have a much smaller squad."
Source: PA
Source: PA