Harry Kane's double helped Bayern to a 3-0 win against Lazio in the second-leg of their round of 16 tie, which sees them reach the final eight 3-1 on aggregate.
Dier, who signed permanently from Tottenham just days ago, enthused: "Given the situation we were in, there was a lot to do for us in this match and I think we handled it really well.
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"There's a long way to go this season and, in the Champions League, anything is possible. We're excited for the quarter-finals, that was the goal.
"I'm settling in very well: the club, the city, the fans have welcomed me very well. And I'm really enjoying this experience, I'm really enjoying playing for this club. I'm just doing my best to help the team."