Burnley's search for a first win since promotion back to the Premier League will go into a 10th game -- a trip to Arsenal next weekend -- as Everton won 3-1.
The Clarets are the only team in the top four divisions of English football without a victory, and manager Sean Dyche felt the Toffees' quality in front of goal was the difference between the sides.
He said: "It was a very challenging game against a fine side decided more or less once again by high-quality players doing what high-quality players do. That was their clinical edge against ours.
"Our general performance was good I thought, particularly first half. Some of our football was very good, and the will and demand to play but also to create chances was there, but that clinical side of the game is definitely where it's at for us at the moment.''
The main positive was a first Premier League goal for last season's top scorer Ings, who became the first Burnley striker to find the net this season.
"It was a very good finish,'' said Dyche. "We know we want to play on the front foot and we did. I thought he should have nicked one at the end but he looked nice and sharp and he's growing again.
"He had a soft start to his season in the Premier League and then getting the injury. Weirdly I thought that might do him good, and he looks nice and lively.
"All the strikers need goals. They're all in there, they're all clambering. We have to keep believing it will come.''
Dyche acknowledged Eto'o's cutting edge up front was the difference between the two teams.
"Samuel Eto'o is a player who has been doing it for many, many years; fantastic player and they bought Lukaku so they have that kind of edge and we're still finding that, we're looking to find that and we have to find that,'' he added.
"Good moments for us generally, but we're not naive we know this is a really tough challenge and a tough league and we know we're going to have to continue working week in week out against some things that don't go for us.''