It was the first time Forest had scored three goals all season, with Ryan Yates adding a third, before sub Ben Thompson netted a consolation for Millwall late on – and it was enough to extend their unbeaten run to seven games.
Ameobi's double provided the foundation for victory as he scored from the edge of the box in the 34th and 70th minutes, with his second particularly spectacular.
"His second was a beauty and he does have that in his locker. This is our request to the offensive players we have got – can you make the difference?" said Hughton.
"We know we are going to have lots of battling games, where we might not have the possession we might like and when that happens, it is down to the quality of your players. Sammy is one of the players who has that.
"I am really pleased for him, but his all round performance was good. The defensive work he did was also really good.
"I think we worked hard for that. If you get the goals in the right moments, it can be your day – and it is the first time this season that we have scored three goals. It was a performance that warranted that, against a very good Millwall team.
"You need those battling qualities, because Millwall have quality in their side. They are relatively direct and you have to be ready for that.
"You have to take your opportunities when they come your way and thankfully we did that.
"In our level of performance, we have not been too far away, in most of our games. The difference has been in those moments. There are teams who have the individuals who produce those moments a little more regularly than we have."
Millwall's consolation came in the 89th minute when sub Thompson forced home a shot from the periphery of the box, as he connected with keeper Brice Samba's punch.
But they have now collected only one win in their last 15 Championship outings and boss Gary Rowett admitted that is a reason for worry.
"Of course I have concern about one win in that period of time. There have been a lot of draws where we should have won the games – but we haven't," said Rowett.
"So I cannot really stand here and say that we should have done this or that, because we haven't done it.
"We have to start getting serious about it. We have to earn the right to win games. We have to fight a little bit harder for the cause, which is what Millwall is all about.
"At the moment we are not showing the right level of consistency. We go to Bournemouth and play really, really well against a very good side, to get a draw.
"Then at Forest, we do not put in the same level of energy and commitment, in my opinion.
"The frustration for me was that we did not match the same energy and effort that we showed against Bournemouth. When we do not perform to that level, we are not the same side.
"We have to be at it, we have to be strong in our shape and not allow easy goals to occur.
"In my opinion, two of their goals were very good goals, but we should not be allowing Sammy Ameobi to get into those areas and the third goal was just a really weak set-piece goal, which bounced in the box and we should have dealt with.
"We did not deserve anything out of the game."