The Blues defeated Galatasaray 2-0 at Stamford Bridge on Tuesday to seal a 3-1 aggregate victory and secure safe passage to the next round of the competition, along with the likes of Real Madrid, Barcelona and Bayern Munich.
And Mourinho is adamant his players deserve to play alongside the world's elite and has backed them to prove it in the coming weeks.
"We are there. It's different than last season because last season was Europa League at a different level," he told ITV. "But to come from Europa League to the quarterfinal of the Champions League is important for the players. Is important for the club.
"We are a club of Champions League and now we are in the best eight, amongst the best teams in the world. We are there.
"The players deserve to be there. This was a difficult tie where people think we have to do it. The reality is not like that. Galatasaray is a big club, with a lot of experienced players and especially away it was a very difficult match. I think we did very well."
Frank Lampard echoed Mourinho's sentiments and is confident he and his teammates can go all the way in the competition, but remains wary ahead of Friday's quarterfinal and semifinal draw.
"It [the performance] was everything we wanted it to be. It was a tough game,” he added. "People take for granted that we got a decent result out there and think we're going to win comfortably here but we knew it was a tough game and I thought from beginning to end they hardly threatened. It was a very controlled, very professional performance.
"It's tough [to win the competition]. I wouldn't make those predictions yet with the amount of great teams left in it as we know. We'll wait and see who we get drawn against. We're confident at the minute. It gets tougher every year this competition but we're still in there."