It is the second game in a row Everton have led 2-0 only to lose, becoming the second club in the Premier League era to do so in consecutive games after Bournemouth two years ago.
They are rooted to the bottom of the table with no points from four games and 13 goals conceded after another horror start to the season that will have fans expecting a fourth relegation battle in a row for the grand old club from Merseyside.
"We were terrific in the last game (a 3-2 loss at home to Bournemouth)," Dyche said. "Today we make a mistake and they capitalise on it. I said to the players, the killer instinct in both boxes is what’s vital.
"The key moment was to go 3-1 up. We didn’t and we made a mistake, and they capitalised on it. We have to keep going.
"We’re making high-quality chances. At the minute, we’ve got to score as many as it takes to win a game. That’s been a challenge since I’ve been at the club. We can’t keep leaking goals like that."
Injuries to key defenders in the early weeks of the season, not least centre-back Jarrad Branthwaite, have left Dyche trying to plug holes.
When Vitaliy Mykolenko was forced off in the first half against Villa, 39-year-old Ashley Young had to switch from right-back to left-back.
"We’re having to manipulate the team. We have to keep believing in each other. You’ve got a responsibility to deal with it – and that’s what we have to do, including me," Dyche added.
"(The players) are an honest group. They’ve worked very hard and been through a lot. We are where we are, so they’re very disappointed. We have to respond."
Everton host Southampton in the League Cup third round on Tuesday before a league trip to Leicester City next Saturday.