Those dropped points saw them fall out of the top four and Moyes knows they cannot afford to allow things to slide again.

“The position doesn’t shame the way the players have been playing they have been doing that well,” he said.

“But we could quite easily have slipped out and been in the bottom half of the league.

“It feels good (to beat Spurs) but we have to make sure we maintain that.”

Despite dominating it appeared their unbeaten home league record – which now stands at 12 – would be ended after Clint Dempsey’s deflected strike gave Tottenham the lead with 14 minutes to go.

However, Steven Pienaar headed home the equaliser in the 90th minute before, 88 seconds later, Nikica Jelavic hit his first goal for a month.

For Moyes it was a welcome return to goalscoring form for the Croatia international.

“There were signs he was getting a little bit better but he looked a bit frustrated because we weren’t getting the ball to him enough,” he added.

“But if he can keep getting the goals, and with Steven getting one, it keeps us moving along nicely.”

The one downside was the loss of Kevin Mirallas, returning from a four-match absence, with a hamstring problem.

Moyes is optimistic it is not a recurrence of the injury which sidelined him for a month but further examination will be required.

“We don’t think he has done his hamstring, he just felt it had tightened up,” he said.

“I don’t think it is bad but the last thing you want to see is the recurrence of a hamstring injury.

“You can see what he offered us in the first half, something which we have probably missed.”

Tottenham manager Andre Villas-Boas was left to bemoan another late defensive calamity, a bad habit which has cost them dearly this season.

“We suffered two goals in the last minutes when there were moments where we looked more in control of the game.” he said.

“It has been quite an adventure in the Premier League this season – if we count the number of results that have been going for us before the last minutes we would be first.

“It is something we are aware of, which is why we speak about it openly, and it is something we have to improve – seeing off games.

“It is not a mental thing, it is the nature of the game because it was our best period for quite some time in the second half.

“You kind of knew as soon as the kick-off went for the 1-1 they (Everton) would go and have a go and they certainly did.

“It is a difficult blow to take.”