The Bayern Munich midfielder scored on his full debut for the Young Lions and starred in a 5-0 rout of Albania on Tuesday.
Nketiah also missed a penalty but the hosts wrapped up their Euro 2021 qualifying campaign and head to the group stage in Hungary and Slovenia in March unbeaten.
And 17-year-old Musiala, who can also play for Germany, has given Boothroyd a selection headache after just two Under-21 appearances for England.
"He gives me a nice problem going into March," said Boothroyd. "I thought Jamal was excellent. You can see that physically he's not finished. He's going to be a brute of a man.
"His brain and his feet are the most impressive, he's razor-sharp. We're really pleased with him to step up the way he has done.
"It's been great to get to know Jamal this week and the players have taken to him. He's a really good player. Hopefully we can persuade him to stay with us and we'll continue to push his development.
"We'll have a look at it now and hopefully everyone will stay fit."
Chelsea forward Hudson-Odoi opened the scoring after four minutes when he cut inside and Marco Molla allowed his shot through his hands.
Leicester's Justin fired in after 26 minutes and Musiala grabbed a third, clipping in after swapping passes with Oliver Skipp just before the break.
Nketiah made it 4-0 early in the second half before missing a penalty, Molla saving his spot-kick having brought the striker down 10 minutes from time.
But the Arsenal forward did grab a second late on – his 16th Under-21 goal – when he cut inside and found the bottom corner.
Boothroyd, whose side had already won Group Three, added: "Despite the scoreline, I was a bit concerned prior to it because we'd not kept a clean sheet in a while. To score five and finish off the campaign like that is really pleasing.
"For me it's not conceding. The strikers might win the games but good defences generally win championships."