Defender Leighton Baines has urged Everton to be braver in front of goal.
The Toffees have been accused of trying to walk the ball in this season, continually passing up opportunities to chance their arm from the edge of the box.
Manager David Moyes has demanded a more direct approach but saw his side again squander a string of chances during Monday night's 2-2 draw at Sunderland.
Tim Cahill and Mikel Arteta scored for Everton while Jermaine Beckford missed a gilt-edged chance to win it at the death but left-back Baines feels he was not the only culprit.
"There was probably a lot of times we got within 20 yards of goal, with no real pressure and still turned down the opportunity to take a shot," he told the Liverpool Echo.
"Sometimes you just need to take the chance and hit one. Sometimes it will fly in, others it will miss, and I think that is something we need to look at. We are in range a lot of times and not hitting it.
An Arsenal goal
"Some of us are always looking for another pass. For example, Steven Pienaar is a footballer through and through, and he is always trying to score a goal that you'd call an Arsenal goal - lots of passes then it's knocked in from six yards.
"We're not doing that at the moment unfortunately, and players like Steven and Mikel can really hit a ball.
"Like with Mikel, his shot took a deflection and went in. You've got to try your luck."
Everton have been improving since a dismal start to the season, losing just one of their last nine.
But Baines admitted Monday's draw was frustrating as the Blues remain just two points above the bottom three.
"We feel we've dropped another two points," he added. "We came to win and we know what three points can do for you at the moment in the league with the table how it is.
No Becks blame
"We were disappointed. They were off the back of a good result and put us under a lot of pressure, so in some ways it wasn't the worst point.
"Becks had a great late chance, and the two extra points would have made a big difference but we can't keep relying on that.
"We can't always ask him to come on for 10 minutes and win a game. That'd be hard on him. We must do more in the 80 minutes before that to put ourselves in a better, winning position."