Moyes’s side host Chelsea and United in their next two games of a testing February, but Neville believes it is on their travels against the Premier League’s upper echelons that Everton must begin producing.

“We need to start winning away to top four sides,” he said.

“We had an unbelievable opportunity at Arsenal and threw it away in the last minute and this was another chance. We’ve gone to top sides and got draws but want the next step now. We’re getting more belief we can come to places like this and win, though. The gap (between Liverpool and Everton) has been closing for a couple of seasons and our performances have definitely been getting better.

“We seemed so near, but the final step is always the hardest and it’s one we are striving for. I don’t think it is a psychological thing, we just needed that bit of quality. That first win will hopefully be the catalyst, but Chelsea on Wednesday is a great game to bounce back in. Them or Manchester United will win the league, they’re the next two we play, so we’re going to have to beat the champions over the next couple.”

Kyrgiakos was dismissed for a two-footed lunge on Marouane Fellaini, who was stretchered off with a shin injury, before referee Martin Atkinson gave Steven Pienaar his marching orders in stoppage time for a second bookable offence. And although lamenting the loss of the influential Fellaini, Neville admits Everton did not have the imagination to find a way through Liverpool’s defence.

“I was at the other end for the sending off but the lads say he (Kyrgiakos) went with his studs up, and you don’t want to see tackles like that,” said Neville. “Felli was a crucial man to lose, but we were 11 versus 10, we’d brought on Mikel Arteta, who could take possession of the ball for us, and we had more of it than previous visits. But we lacked the quality and guile in the final third.”