Tarkowski, who signed Dyche when he was at Burnley, said he hoped victory could help turn prospects around for Everton, who had won only three league games all season before Saturday.
He told BT Sport, “It’s been tough for us and the fans and all the staff at the club. Hopefully this is the turning point for the club, there’s a lot of talent here.”
“It’s taken me a while, I need to score more. What a great time to do it and have a good day. Back to work on Monday and we move on.”
“Sometimes we lack that little bit of patience and that’s what the fans want. We’ve seen what happened today.”
It was the first time that Everton had beaten a top of the table side in 11 years, their last such win having come in January 2012 against Manchester City.
Toffees winger McNeill said: “We know how good they (Arsenal) are as a team, but we also know how good we are as a team as well as the number of chances we had.”