The Potters boss was disappointed not to take anything away from Goodison Park but remains upbeat ahead of a potential relegation battle at the Britannia Stadium
The Potters have been in poor form of late, winning only one league game since the turn of the year but put in one of their better away performances this season at Goodison Park, creating a number of chances either side of Kevin Mirallas' winning goal.
"We haven’t played many games where we haven’t created any chances, and that was the case again today," the Welshman told the club's official website.
"Obviously it is a bit of a worry, because we had more than enough chances to have got a point from the game, or even won it."
The defeat was Stoke's fifth in six matches and leaves them just four points off the relegation zone despite being within touching distance of the European places at the end of December.
"You sometimes have a run of games where these things can happen," Pulis continued.
"Unfortunately for us, we are on one of those runs right now. You just have to make sure that the lads remain confident and believe in their ability.
"We have come here today and played against a very good Everton side, who I have always said will challenge for a top-four spot this season, and we feel aggrieved to be leaving here with nothing."
Stoke's next match sees relegation rivals Aston Villa come to the Britannia Stadium where a win for the visitors would close the gap between the two sides to just a single point with six matches left to play.
"We need our fans behind us as much as ever for that game," Pulis added. "They make the difference for us, there is absolutely no doubt about that.
“I said the other day that our four home games will dictate things for us, and I stick by that. We aren’t panicking here though; I have said all along that this will be a tough season for us.
"We need a win, and we will do everything we can to make sure that we get that against Aston Villa next weekend."