Barry has failed to register for the Blues in 13 matches so far this term, despite netting 19 times last season for Basel and Villarreal.
Earlier this week, Everton were linked with a move for Al-Ahli striker and England international Ivan Toney as Moyes tries to fix his toothless attack, which have led the side to 13th place this season and just 12 goals in 11 games.
Moyes says Barry must step up
The Toffees win over Fulham at home was perhaps Barry’s most encouraging performance, even if he did not find the back of the net. Moyes commented on his time on the pitch and says the 23-year-old must push to get himself on the scoresheet.
The Blues boss told evertontv:
“I thought Thierno had his best game for us. We need him to keep stepping up all the time, we need him to up his ante all the time.
“There’s a great history of number nines at Everton Football Club and it’s not an easy thing to follow when you go back through time.
“Let’s hope maybe we can give him a little bit of respite. He’ll get more confidence from his performance, he’ll get great confidence from the support he had from the crowd.
"It was a great, great way to see him because everybody knows we want him to do well. And he performed well, he really did.”
Barry sends message to fans
Barry received a standing ovation from the crowd after what was his fourth start since signing for the club. He spoke on social media after the game as he begins to bond with supporters who clearly think he has the quality to be in the side.
“There are things that mean more than goals.
“With my difficult start to the season without scoring, receiving an ovation from you today really warmed my heart and showed me that I’m on the right path.
“Once again, thank you so much!”