The holders have had two close calls against Accies in the last 10 days, firstly being forced to battle for a 3-3 draw in the cup and then only just scraping a 1-0 win in the SPL at the weekend.
Both those games took place at New Douglas Park, and Smith is expecting a much better display from his players in front of their owns fans at Ibrox.
"We would hope that home advantage would be a big thing for us," he said.
"In recent seasons we have had some decent wins against Hamilton, although they've had to be good performances to get there.
"Hamilton are a really well-organised team, they try to play some good football and they are not an easy team to play against overall."
Hamilton have conceded 18 goals in four games at Ibrox over the past season and a half, losing in both cup competitions there last term. But manager Billy Reid believes his players have every right to go there with confidence.
"We have acquitted ourselves very well in both games and I think we can count ourselves slightly unlucky on Saturday."