Marco Silva accepted hostility from Everton fans was justified as the Toffees suffered a fourth consecutive Premier League defeat.
Jeff Hendrick’s 72nd-minute goal was enough for Burnley to secure a 1-0 win at Turf Moor, with the visitors reduced to 10 men with more than half an hour remaining when Seamus Coleman was shown a second yellow card.
It is Everton’s worst run in the league for nearly five years and the visiting fans directed their anger at Silva after the final whistle.
The Portuguese labelled the next game against West Ham in a fortnight as a must-win, and said of the supporters: “They will keep supporting us, I have no doubts about that but, if you are asking if they should be angry with the team and with myself, then of course, that is normal.
“In the last four games we didn’t get the results and they have all the reasons to be angry with us. It is up to us to work harder, to be braver, to be more clinical and our attacking players need to be more aggressive and assertive in these type of games.
“We had so many dangerous moments around their box and we have to make better decisions. Our confidence is not the best at the moment.
“I understand 100 per cent why they (the fans) are angry with us but we have to stick together and the next game is a must-win game for us. Last season we had a worse moment than this one and we reacted fantastic. I have no doubts we are able to do that again. We must win the next game.”
Silva confronted referee Graham Scott after the final whistle and felt Coleman’s second yellow, for jumping into Dwight McNeil, was questionable.
“The second yellow had a big impact on the game,” the Everton boss said. “It looked a harsh decision, a really harsh decision in my opinion. After that the game was more difficult for us but our opponent didn’t have big chances. In one set-piece they scored and that detail made all the difference.”
Burnley boss Sean Dyche argued that Coleman was fortunate not to see red for his first offence, when he caught Clarets left-back Erik Pieters with his studs low on the Dutchman’s leg.
“He’s not that type of player at all but the first one, it’s not a great challenge, let’s put it that way, and probably in the modern way that the game is, it’s a red,” said Dyche.
“By the time the second one’s come round, the ref’s really got no choice.”
Pieters initially carried on but hobbled off 10 minutes into the second half.
“It’s a sore one, that’s for sure,” added Dyche. “Hopefully it’s not too serious.”
The victory made it four games unbeaten for Burnley, who found themselves in the top four after Saturday afternoon’s matches.
Dyche acknowledged this was not their finest footballing performance, saying: “From a management point of view, credit to Everton because they opened up the pitch even more than they were trying to do, threw caution to the wind and it kind of put us out of kilter a little bit, and that sometimes happens with 10.
“It’s a strange thing with 10, sometimes you completely dominate and sometimes it becomes tricky, and today was a tricky one.
“We’ve got to find moments but equally we’ve got to do all the hard stuff, all the ugly stuff like all teams have, but sometimes we have to do it more.
“We had to show grit, determination, organisation and still find the moment to win a game.”
