The Slovenian side head into the Group J encounter second in the group table with three points, having thrashed Panathinaikos 3-0 at home on matchday one.
Milanic knows his side will have to put on a similarly impressive performance when third-placed Spurs visit the Stadion Ljudski vrt on Thursday.
Andre Villas-Boas' side are looking for their first win in the group after two draws and will be hoping to repeat the success of Birmingham, who last season beat Maribor home and away in the competition.
"We have played against three clubs from the island in recent years - Hibernian, Rangers and Birmingham - but Tottenham have more qualities and are different,'' Milanic said.
"They have speed and skill. From our side, it is clear that we want to attack, but in these moments we must pay attention.
"Our competitors have a quick transition from defence to attack so that even in moments when one of our players will not be involved in play, he will have to think two moves ahead."
Maribor will be without Nejc Potokar and Rajko Rep on Thursday through injury, while Jovan Vidovic is ineligible.
Gareth Bale and Emmanuel Adebayor will be missing for Tottenham in what Villas-Boas believes will be a "decisive" double-header with Maribor.
"I think these two games with Maribor is going to be the decisive point of the group phase," Tottenham boss Villas-Boas said.
"A point will not be a bad result as it will keep us tight with Maribor. Lazio can escape if they beat Panathinaikos tomorrow [Thursday].
"But our two games with Maribor will be decisive. After those we will see where we stand, before we have a home game with Panathinaikos and a difficult trip to Lazio.
"I think these two games could prove decisive. You will get a clearer picture after these two games to see more or less what can we do."
Maribor were defeated in the group stage by second-tier Birmingham in last season's competition and asked whether they were a side Tottenham should be beating, Villas-Boas said: "Yes, for the players we have and the team that we have this is clear.
"But it doesn't always go like that and that is the reality of the game. You saw only yesterday Manchester United struggling against Braga - two teams of completely opposite dimensions.
"By the nature of the game, we will not expect an easy game. It is a passionate environment, a very, very good club that are run tremendously and have done very well in the last 10 years, winning most of the Slovenian titles."