Sam Allardyce felt Everton "gifted" victory to Burnley after his struggling side were beaten for the fifth successive away game in the Premier League.
Cenk Tosun's first for the club gave the Toffees a 1-0 half-time lead at Turf Moor, but goals from Ashley Barnes and Chris Wood secured a first win of 2018 for the Clarets, Ashley Williams' late dismissal capping a bad day for Everton.
Gylfi Sigurdsson missed a good opportunity before Wood's late header won it for the hosts and Allardyce bemoaned poor decisions at both ends of the pitch.
"We lost it by not scoring the second goal when we had clear, clear opportunities. At least three in the first half," he told BBC Sport.
"Burnley hadn't won in 11 and if we went 2-0 up it would have been hugely difficult for them.
"We gifted them a goal which lifted the spirits around the ground. And I always dislike conceding from a corner, it could be avoided.
"That's five away defeats on the trot. It's simply not good enough.
"I feel worse than the fans - they won't believe this - but it's my responsibility. I go home and say to myself 'how do I put this right?' For me to see the players under perform in the second half is very disappointing for me. It's my problem to sort it out."
Williams in particular drew the ire of Allardyce, the defender facing a three-match ban after elbowing Barnes.
"Ashley Williams getting sent off sums our day up," added Allardyce. "It shouldn't happen, he's swung his arm and he's an experienced player."
Dyche's 250th game in charge of Burnley proved a landmark in more ways than one, the Clarets coming from behind to win in the Premier League for the first time in his five-year reign.
"I don't think it was anything to do with my 250th game," Dyche said. "It was a fantastic performance. We have not been far off in a lot of these games. It was a thorough performance and winning one.
"Some quality moments in it, especially the pass from [Matt] Lowton [for Barnes' goal]. It was as good a pass as you will see.
"We have to be resilient because it is hard work for us in the Premier League. But that will and demand, the players here have underling honesty to what they want to achieve. They didn't go down after going behind and the second half response was excellent.
"I said at half-time to the players that they had nothing to lose. At the break I didn't want to wait. I wanted to be proactive. We have more to do. We wanted to correct the run and we have done that. Hopefully that freedom in the second half is something we can carry on."
- World Cup 2023: England team preview, squad, key players, form and prediction
- India vs South Korea LIVE Score, Asian Games 2023 hockey semis: Hardik, Mandeep, Lalit score as IND leads 3-1 vs KOR after first-quarter
- Asian Games 2023 Live Updates, October 4: Lovlina gets silver in 75kg boxing, IND 3-0 KOR in hockey semifinal; Jyothi-Ojas bag archery gold
- Asian Games 2023: Lovlina Borgohain wins boxing silver in women’s 75kg
- Asian Games 2023: Overall medals tally October 4 - LIVE - India 4th with 74 medals, 16 gold; Lovlina gets silver; Ojas-Jyothi win archery gold; Eye on Neeraj