The Latics goal came in fortuitous circumstances as Phil Neville's spinning deflection from Jean Beausejour's cross wrong footed Tim Howard for the opener.
In typical fashion the Latics failed to keep a clean sheet and Victor Anichebe took just seven minutes to find the Toffees equaliser.
Speaking about the game, Roberto Martinez told the club's official website: "I told the players after the game that we need to keep doing the right things and we'll get the rewards.
"We all get anxious during games and in the build-up and there is plenty to be said from the outside about our position in the league.
"But we need to build that siege mentality at the club and not let anything affect our performance. The team looked as though they were back today, ready to fight and ready to compete which is very pleasing.
"It's a point that we've come away with that doesn't reflect the true dominance of the game we had, and now we need to get ready for Bolton next weekend."
The Latics boss was particularly pleased with the home debut of Jean Beausejour who joined from Birmingham City just days before the close of the transfer window.
Martinez added: "It was very impressive to see Jean Beausejour have that kind of debut at home, and as a group we saw plenty of desire which I enjoyed watching."
Next up for the Latics is the trip to neighbours Bolton in what is a real relegation six-pointer.
