They have won just five games in 62 matches against the top six in the last 10 years and the Toffees' stand-in captain in the absence of Phil Jagielka believes that has to change.
And Zola says they will only improve as they learn to cope with new manager Maurizio Sarri's unique methods.
'If he's not fit it's a good opening for another player to play in that position'.
"I think they can play together, but I think Loftus-Cheek has got to play one of the wider roles if Barkley plays, where your [Eden] Hazards, Pedros and Willians are", he added.More news: NASCAR Might Take Away Wins If Teams Keep Cheating Next Season
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BATE Borisov hit the woodwork three times in Belarus, where Giroud ended his drought seven minutes into the second half with a near-post header from a left-wing cross by Emerson Palmieri, who had been found by Jorginho's pass. We didn't manage the last 15 minutes well.
The Blues were beginning to pose a constant threat but just before the hour mark, Mikalay Signevich nearly found an equaliser for BATE with the striker seeing a shot hit the underside of the crossbar after he had got in the way of a miscued effort from distance.
The France global headed Emerson's cross in at the near post early in the second period to maintain the Blues' 100% Group L record.
Apart from this spectacular string of results, Sarri has also introduced a more enterprising brand of football at Stamford Bridge.
"It's true that I was hoping to score soon, because I came back late from the World Cup and after I lacked a bit of efficiency and luck sometimes", he said. "You always have to work hard and keep the faith". And so for his confidence I think it's very important. "He is very important for us", the Blues boss said.