Aki was ordered off by referee Nic Berry after 29 minutes for a tackle on Ulupano Seuteni at Fukuoka Hakatanomori Stadium, where Ireland needed a bonus-point win to be assured of a place in the last eight on Saturday.
Ireland were already in command at that stage following tries from captain Rory Best, Tadhg Furlong and Johnny Sexton.
Sexton's second try secured the bonus point just before half-time and Ireland dominated the second period, with Jordan Larmour, CJ Stander and Andrew Conway also going over.
Aki is set to be suspended for a quarter-final clash with either New Zealand or South Africa next weekend and head coach Schmidt was left with a bittersweet feeling after watching his side secure their passage from Pool A.
"...well we had a home game tonight as you could see..."@IrishRugby head coach Joe Schmidt praises brilliant Irish crowd after his side secured their place in the quarter-finals with 47-5 win over Samoa at #RWC2019#IREvSAM #RWCFukuoka pic.twitter.com/sJ4jw21Fx2
— Rugby World Cup (@rugbyworldcup) October 12, 2019
"We're obviously happy with the result and with a number of things about the performance, but we're obviously disappointed we didn't manage to finish the game with 15 players and we'll look at that and try to come up with what we believe is some reasoning behind that," said the New Zealander.
"I'll have to review it and have a really close look. I rate Nic Berry, I think he's a very good referee, the TMO tonight Rowan Kitt is a very good operator so it's hard to argue at the moment, but it's pretty devastating for Bundee.
"He knows a lot of the Samoan players very well, I know they've got a lot of respect for him. For us it's really disappointing."
Skipper Best was proud of the way Ireland coped with being a man down.
"We've overcome red cards before, it's never ideal but I think it shows a lot of character about the squad, if you go down a man, how you adapt to that," said the hooker.
"Ultimately there was no panic, there was a lot of collective and we continued to attack them."
Photo Getty Images Caption: Bundee Aki is sent off by referee Nic Berry