Jesus injured his knee while playing for Brazil at the World Cup and he is due to be out for around two more months.
Nketiah has led the line for Arsenal in Jesus’ absence and the striker has done well, scoring in each of his last two games.
The Gunners’ attack has looked sharp during those matches, scoring seven goals and winning both games to open up a seven-point lead at the top of the Premier League.
“Everyone has to step up,” said Odegaard. “We are missing a great player but you see the quality that Eddie has.
“Two goals now and everything that he brings in the game also. You see the front players we have, we are always going to create chances and be dangerous, and it is just about getting the players in the right positions and good things will happen.
“When a player like that (Jesus) is injured you will always miss him. He has great quality and great personality. He still gives us a lot outside the pitch. The energy he gives and everything at the training ground he still gives a lot.
“But all the players need to step up when you miss someone like that and we have done excellent. Credit to Eddie to come in like that and perform like this. It is amazing to see.”
Odegaard has also been in fine form since the Premier League returned on Boxing Day, scoring two goals and laying on three assists.
The midfielder was one of those who did not go to the World Cup as Norway failed to qualify, and he instead took part in some warm-weather training in Dubai.
Odegaard believes he is feeling the benefit of that, having helped him to hit the ground running for the restart.
“I would have preferred to have been there [at the World Cup],” said Odegaard.
“I was disappointed not to go there with my country. But I used it in a good way. I had some rest and time to work on different things. I feel good now so I am happy with what I have done.”
Arsenal are in the driving seat in the title race and they could go 10 points clear of Manchester City if they beat Newcastle on Tuesday, but Odegaard insists they aren’t getting carried away.
“We don’t focus on that, we focus on every game to improve and get better,” he added.
“And of course we are in a good position and we are really happy to be there. It is our job to keep fighting and keep improving and make sure that we can fight all the way.
“Missing the Champions League [last season] was a big disappointment for us and we said before the season that we were really hungry to come back stronger and better.
“I think we have done that and we are in a good way and improved in a lot of areas with the ball, without the ball and in front of goal, own box, a lot of things we have improved.”