Australia hold an unassailable 2-0 lead in the three-Test series.
"You want to try and wrap up the series 3-0," Smith said.
"They fought really hard to the end.
"I'm sure they're going to come out hard in Sydney again. We're going to have to be at our best if we want to win."
Combined with South Africa's struggles against England in Durban, the result put Smith's men one step closer to the No.1 ranking they crave so dearly.
Australia are currently third on the table on 109 rating points, with India (110) and South Africa (114) both ahead.
A two-Test tour of New Zealand in February will be a more realistic gauge of where Australia are at.
However, West Indies showed a lot of resolve with the bat in Melbourne.
It is the first time they have batted more than 80 overs in both innings of a Test since 2012.
"I don't think we dropped," Smith said.
"It was a tough wicket to take wickets on, you really had to grind it out and work extremely hard.
"West Indies were up for the fight this game. They improved quite a lot from the last match and hopefully they can continue to show that fight."
Jason Holder top-scored with 68 and vowed his side would show more of the same fight.
"We have been criticised from all different angles but I've just stressed to the team to keep faith," Holder said.
"This shows what we can do if we apply ourselves.
"We just need to keep that belief and keep pushing Australia.
"You could see guys really trying to play themselves in. If we continue to do that we'll show better signs in the third Test match."
Josh Hazlewood failed to take a wicket in the Boxing Day Test, while Peter Siddle was clearly restricted by an ankle problem.
Hazlewood and Siddle will be assessed when the squad trains in Sydney on Friday.
Marsh stepped up sharply, sending down 17.3 overs and regularly hitting the 140 km/h mark.
The allrounder dismissed Marlon Samuels, Denesh Ramdin, Taylor and Holder.
"It's probably as well as he's bowled in Test cricket," said Mark Taylor on the Nine Network.
Lyon also proved a partnership breaker.
Lyon added the scalps of Kraigg Brathwaite, Jermaine Blackwood and Carlos Brathwaite to his first-innings haul of four wickets.
"I'm trying to improve every day," Lyon said.
-AAP