The 26-year-old joined the London-based side in a season-long loan in August but is yet to hit the back of the net after eleven Premier League games.
Ayew was a second-half substitute when Chelsea defeated Palace 3-1 at Stamford Bridge on Sunday and once again, his contribution wasn't impressive upfront but his manager is hopeful of a turnaround of events as the season wears on.
"I am not concerned in the sense that I am worried that these two players [Ayew and Alexander Sorloth] don't understand what their jobs are and what they need to do to get better and score some goals, I am not worried at all," Hodgson said, as quoted by Football.London.
"But of course, I shall be more than happy, like all supporters of my club, when those goals start to go in, because it will be great for the player concerned and his confidence will grow, and he will feel it is reward for the work he is putting in each day on the training field.
"Absolutely, he needs to continue believing in himself, like all these players," Hodgson said.
"I don't know if it happened this year, but for the last two years in the first six or seven games, Harry Kane was being held up as someone who has lost it because he hasn't scored in the first half a dozen games. That's the way it is.
"I tend to look longer than that and I think that if people have got the ability, they will come good."
"And I am glad to hear that he [Ayew] believes in his ability and I am glad to hear that he feels if he keeps working hard and doing the right things, he will turn it around.
"I don't think we should be dismissing people because they haven't scored the goals. It is still early on in the season and the season is quite long and we will need all of the players we have got in the squad because we don't have a massive squad in depth," he added.
Ayew is expected to mark his return to international duties this month after more than a year away when Ghana play Ethiopia in the 2019 Africa Cup of Nations qualifiers.