Iliman Ndiaye gave Everton an early lead before Stephy Mavididi found a second-half equaliser.
It marked a first point for the season for the Toffees and Dyche later said: "Very positive display. We had chances that went begging again unfortunately, which we have done too many times in games where we should be killing them off. We didn't manage to do that today but a lot of positives to take.
"James Garner was ill and got thrown in last minute and played excellently, Youngy and Illiman produced some superb play for the goal, lots more positives.
"Unfortunately you come away from a game where you probably should win with just a point. Normally you would be pleased with a point but at the moment we would have loved that win obviously."
On his players' character, he continued: "It is just noise you know? The players are human beings so naturally it does effect you but the point is that it is just noise. I've told them that we have been through this before, had challenges before, had a lot of knocks and the players have been grinding through.
"Today was not a grind. There was some really good play and we affected it in a really good manner. We opened them up enough times to win the game but you've got to score another goal."