The 24-year-old’s shot was deflected into the net by Leighton Baines in the 14th minute, with the striker running towards Moyes and swallow diving in response to the manager’s pre-match comments about Suárez’s record of simulation.
Shortly after, the former Ajax man netted from Steven Gerrad’s free-kick before Leon Osman and Steven Naismith restored parity in a blistering 13-minute spell before half-time.
“I thought it [Suárez’s celebration] was great,” Moyes told BBC Sport.
“I actually quite liked that and it’s the sort of thing I’d have done if I’d have scored.”
However, the Toffees boss did feel referee Andre Marriner should have shown Suárez a red card for a tackle from behind on French defender Sylvain Distin in the second half.
“He was a very lucky man to stay on the pitch for his tackle,” Moyes added. “Definitely. It’s over the top, down the back of the leg.”
However, Liverpool manager Brendan Rodgers defended the Uruguay international’s challenge, insisting it was not intentional.
“I didn’t think it was a red card,” he said. “Sometimes you get that with a striker, when they are just a fraction late. They are trying to time it just as they pass it.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news