The Blues romped to a 6-0 win over the Slovenian champions at Stamford Bridge last month and victory in the return fixture could seal their place in the knockout stages with two games to spare.
"I like this concept of going with a big club, full of big players to a country, a stadium, a city where normally they don't come," said Mourinho.
"To come here, to play here, I think we have responsibility to play for us and also to play for the people.
"I know they want to win - they don't want us to win - but to play for the people is to play well, and to show what we can do, to show the quality players we have, to show the quality team we have."
Mourinho insists he would never select a weakened team in anticipation of defeat, in a slight made towards Liverpool manager Brendan Rodgers.
Rodgers rested key personnel, including captain Steven Gerrard and playmaker Raheem Sterling, in the 1-0 defeat at defending European champions Real Madrid, but the Reds boss denied he was forfeiting the match.
Mourinho, whose side visit Anfield on Saturday, said: "If Liverpool decide to rest players when they play against the European champions, it's a question for the Liverpool manager - it's not a question for me.
"I don't speak about Liverpool. I speak about myself. If one day I go to a game and I don't feel I can win, maybe I don't go.
"Normally, against the most difficult opponents, normally I will try to go with my best team."
Mourinho is taking nothing for granted against Maribor and described the Stamford Bridge result as "fake".
"The 6-0 win is a fake situation," he said. "Normally Chelsea to score goals needs a lot (of chances).
"Everything went in our direction. The first opportunity we had was a goal, the second one a goal, and so on.
"(But) I know they are a good team. I analysed them against Sporting and Schalke.
"I need to convince the players that the game at Stamford Bridge was one of these matches where everything goes in our direction."