The Belgian champions went undefeated across their final three matches in Group D, coming from three goals down to draw 3-3 at Arsenal and defeating Galatasaray 2-0, before clinching a late 1-1 draw away to Borussia Dortmund on Tuesday.
After Ciro Immobile gave Dortmund the lead just before the hour-mark with a sharply-taken goal, Aleksandar Mitrovic clinched a share of the points for the visitors in the 84th minute, heading Anthony Vanden Borre's cross home at the back post.
Anderlecht sit third in the Belgian Pro League after 18 rounds, having slipped behind Club Brugge and Kortrijk over the past three weeks, but Hasi is confident his team can win silverware this season if they maintain their Champions League form in other competitions.
"Tonight I expected my lads to make up [for poor league performances] and that's what they did," Hasi said, according to uefa.com.
"It was important to make amends but now we have to confirm this good performance against less glamorous opposition.
"If we continue like this, we can still go places this season."
Anderlecht have lost on the road at mid-table clubs Mouscron-Peruwelz and Sporting Charleroi in their past three league fixtures, while they were held to a 2-2 draw at home by rivals Club Brugge.
But with a Belgian Cup quarter-final first leg coming up next week, plus the UEFA Europa League, which Anderlecht qualified for after finishing third in Group D of the Champions League, Hasi is excited about what could happen in 2014-15.
"This Champions League campaign has been extraordinarily positive, I want to congratulate my players on it," the Albanian said.
"It has showcased our football, something we last had at Anderlecht in 2000-01. We must not forget that we have one of the youngest sides in the Champions League and at times we were able to play refreshing attacking football.
"Now we wait to see who the draw pits us against in the UEFA Europa League but first we will focus on the Belgian Pro League."
