The Swedish champions stunned Olympiacos 2-0 thanks to a pair of goals from captain Markus Rosenberg to leave all four sides in Group A with three points after two matches.
Hareide felt the vocal home crowd were crucial in the win and said afterwards: "It is always good [to celebrate with them].
"It is small margins in football. One day you are a hero. The next day you are an idiot.
"But it is not only me, it's the whole staff that works for me and the players. And the fans. The whole city. That's the strength of Malmo.
"Teams that come here are very surprised by the crowd. It is not just the hardcore fans, but all the stadium. It is unbelievable.
"Everybody is behind the team. It is fantastic, and the players feel this.
"It [will] be difficult [to get through the group]. The home games will be important."
Malmo's other home matches in the group, against Atletico Madrid and Juventus, are likely to be crucial.
And goalscorer Rosenberg is convinced they will be a match for anyone at their own ground, including the Spanish and Italian champions.
"We're strong at home. We won against Sparta Prague, Salzburg [both in qualifying] and now Olympiacos," he said.
"We know we can beat every team here.
"Our ambition has always been to get through even if nobody believed that.
"Nobody believed in us when we said we wanted to get into the Champions League but now we're here, we know we can do big things here.
"We're going for nine points at home and hopefully some bonus points away."
