Cameron Jerome's tremendous solo effort cancelled out Peter Crouch's first-half own goal, but the Scot believes his outfit could have taken all three points against the Potters
An own goal from Peter Crouch opened the scoring just seconds before the break, with the visitors the team on top. The hosts, however, came out of the dressing room stronger and following a bold move to bring all three substitutions on at once by Tony Pulis, replacement striker Cameron Jerome latched onto a ball through the middle to finish an outstanding solo effort and equalise for Stoke.
Moyes thought his men played well enough to earn a win, but, admits a point at the Britannia Stadium is a positive result.
"I thought that we played very tonight and that we were maybe a wee bit unlucky not to take a bit more from it, but taking a point here isn’t the worst result," Moyes told reporters.
"I thought we played some really nice football at times, kept the ball well.
"But it's always hard breaking Stoke down and they're always a threat, and they were a threat, two or three of their throw-ins went in and were headed just over the bar, so that was close.
"Second-half, Stoke got better, but always thought we were always liable to score another, but we just never quite crafted it at the end.
"If you’re not on your guard, they can catch you out and we were just caught out and their goal was fortuitous, I'll use that same word again because theirs took a deflection from [Phil] Jagielka."
The point all but confirmed Everton a top 10 finish and is an outcome of the season the club’s manager is proud of.
He added: "If we can just keep trying to win them I’ll be pleased that we finish in the top 10, tonight’s point might just get us in the top 10.
"If you’d have said to me at the start of the season, I'd have said: 'I'll that all day long'. Certainly with our form from January we're better than top 10, but start of the season I'd have said: 'No, I’m happy with that.'"
Moyes' opposite number, Pulis, said of the game: "I thought Everton were the better team first-half and without a question of a doubt, the [Everton] goal is fortuitous, but they deserved that.
"Second-half I thought we came more into the game, we looked little bit tired and a little jaded first-half, second-half I thought we deserved to get a point.
"Give Everton some credit, they've just come off the back of beating Fulham 4-0, they've gone to Old Trafford and got four goals, they're a good side, a top, top team. It's a great result for us tonight."
On his triple substitution that brought about the goal, he added: "Sometimes you get them right and sometimes you don’t, standing here I’m no genius."
Stoke's last two games of the season will be against teams fighting for survival and Pulis is fully aware that his players need to be on their toes.
"We've got two cup finals coming up now, QPR away, that'll be a bear pit there Sunday, and we have to be right and we have to be ready for it.
"Of course the last game of the season which is against Bolton, again Bolton could be fighting for their lives, so two really tough games for us."