Batshuayi, while away on international with Belgium after scoring against Belarus, claimed he was not trusted by Hodgson at Palace.
Hodgson challenged the Chelsea loanee, who had scored just one goal for Palace all season before Monday, to make an impact in the Premier League rather than small nations at international level.
The striker duly responded at Goodison Park and now his manager hopes Batshuayi can kick on during Palace’s season run-in.
Asked if Batshuayi had backed himself up, Hodgson said: “Absolutely. We know Michy is a goalscorer. That is why we took him to the club.
“Since he has come back from Belgium he was happy with his goals against Belarus, that cheered him up because he has not had as much encouragement for a while with us.
“But I am hoping now, with eight games to go, there will be plenty more opportunities to get on the field and show what he can do.
“Because there is no doubt he is a very talented footballer and a player, if we can get the ball to him in the right areas, is capable of scoring, as he showed by converting that chance.”