Arsenal wasted a chance to cement their place in the Premier League's top four as the Gunners were held to a 0-0 draw by Everton on Tuesday.
.
Arsene Wenger's side would have moved four points clear of fifth placed Tottenham with a win at the Emirates Stadium.
.
But they were forced to settle for a point as obdurate Everton's physical approach succeeded in frustrating the hosts.
.
Third placed Arsenal are now two points clear of Chelsea and Tottenham in the race to qualify for the Champions League.
.
However Arsenal still have plenty of work to do as Chelsea have two games in hand on Wenger's team, while Tottenham have played a game less than their north London rivals.
.
"The game was basically down to physical intensity, it was unbelievable from the first to the last minute," Wenger said.
.
"The referee let a lot go unpunished. I think Darron Gibson could have been sent off. He got away with a few tonight."
.
Everton remain in sixth place, two points behind Chelsea having played two games more, and a spot in the Europa League now looks their best bet.
.
"We weren't going to let Arsenal stroke the ball around with 500 passes, we were committed and made some tackles," Moyes said.
.
"Believe it or not that's allowed in football. Some of our defending was top-class."
.
Moyes' men should have taken the lead in the opening moments when Steven Pienaar eluded the statuesque Bacary Sagna and raced onto Seamus Coleman's pass.
.
But with just Wojciech Szczesny to beat, the South African midfielder lifted his shot high over the crossbar.
.
Despite admitting he had rushed Jack Wilshere back from an ankle injury too quickly, Wenger gave the England midfielder his second appearance in four days.
.
And the Frenchman was wincing as Wilshere came in for some rough treatment in the early stages.
.
Crunching challenges from Ross Barkley and Kevin Mirallas left Wilshere writhing on the turf while Wenger leapt to his feet to berate referee Neil Swarbrick for failing to afford his player more protection.