Hodgson impressed by Batshuayi debut
Batshuayi, who signed from Chelsea on transfer deadline day, only played eight minutes from the substitutes' bench in his side's 2-0 home Premier League win on Saturday.
But that still gave him enough time to force a stunning save from Sergio Rico, with the rebound converted by Jeffrey Schlupp after 87 minutes to seal the victory.
Captain Luka Milivojevic had earlier given Palace the lead from a penalty conceded by Cyrus Christie, a first win in four league games for Hodgson's men moving them further clear of the bottom three.
"Michy Batshuayi did so well to create the second goal," Hodgson said after the match.
"We will need these players who came on. We look more dangerous from corners - there are positives for us.
"Second half we played well, first half I have to give Fulham credit, they were very good and we were fortunate. It was a strange penalty, I can't understand what has gone through the defender's head.
"We controlled the game after that and had opportunities. We were not under pressure. But these are anxious times. If we had more points on the board, points that we deserved, it would be less problematic here. Every point is so valuable and if you're in the lead you can stop playing and worry about the final whistle."
Batshuayi himself added: "It's a very important win, it's good for the team and for me too. I feel good to be here but I need to train with the team. It's a good start.
"I met my team-mates today! I will bring as much as I can to help the team to win."
"I met my team-mates today! I will bring as much as I can to help the team to win" - @mbatshuayi #CRYFUL pic.twitter.com/RVG9F70HSX
— Premier League (@premierleague) February 2, 2019
Fulham failed to register a shot on target, but had seen Aleksandar Mitrovic squander a golden early chance. Manager Claudio Ranieri felt the penalty, conceded when Christie handled while challenging Christian Benteke in the air, was decisive.
He said: "The first half was good until the penalty, we had the match in our hands. We controlled the match. The penalty changed the match.
"They deserved to win in the second half, they were better than us. They had three or four chances - well done to Roy. The service to Mitrovic was not good enough."
Fulham have only picked up two points from 13 away games in the top flight and sit seven adrift of safety.
But Ranieri added: "We were in trouble from the beginning [when I took over] but we will continue to be positive, be strong. It's important to be optimistic. We have a target in our mind."
pic.twitter.com/RvGsDyYPWY
— Crystal Palace F.C. (@CPFC) February 2, 2019