Cape Town - "It'll be a test of how far we've come at an international level, how far the guys have developed and improved," Di Matteo said.
"Obviously Real are the favourites over the two games but I think we have a bit more experience of these games now and hopefully we can show that tomorrow."
Di Matteo replaced Jens Keller as Schalke manager in October and guided the German side to a second-placed finish in their group behind his former team Chelsea.
The Italian has already proven that he can upset the odds on this stage, having led Chelsea to their first Champions League title in 2012 by beating Bayern Munich in the final in a penalty shootout.
"That's experience but that's the past," he said on Tuesday.
"I'm coaching a different team now and we're playing against the current Champions League holder - a great team. So I think it's a different situation.
"We just want to show that we've improved - that we're a better team than in the past."
Schalke have no fresh injury concerns following a 1-0 defeat at Eintracht Frankfurt on Saturday and they also have former Real Madrid striker Klaas-Jan Huntelaar available again.
The Dutch international, who has been serving a domestic ban, believes the Bundesliga outfit have learned from the five-goal loss against Real Madrid last season.
"I think in that game we made a few mistakes at the start and we conceded a goal too," he said.
"But at the same time I think we had some good moments, like with Julian Draxler's chance.
"It could have been 1-1 then but once we went 3-0 down we lost too easily."
Huntelaar, who scored Schalke's consolation goal in last year's first leg, has also taken solace from their two league draws against Bayern Munich this season.
"I think at the moment we're playing a different system that's brought us some stability," the 31-year-old said.
"In the last game against Bayern we played that way too and Bayern are a top team like Real. We're pleased about it and it's made us stronger I think."