Having fallen 2-0 behind on aggregate in the second leg at White Hart Lane on Thursday a Christian Eriksen free-kick and a quickfire Emmanuel Adebayor double turned the tie in favour of Spurs.
Now, with a last-16 clash with Benfica to come, Tim Sherwood's side return to domestic matters when they welcome struggling Cardiff to north London on Sunday.
Following last weekend's disappointing 1-0 defeat at Norwich, fifth-placed Spurs cannot afford to lose any further ground on the top four but Dembele is still striving for success on both fronts.
"A club like Tottenham are up there with the top teams and I think they have to be in the Champions League," he said.
"I play with these players every day and of course it is my opinion, that we need to be in the Champions League.
"There are a lot of good teams in the Premier League and we have to work hard to reach the top four.
"We want to win something, too, and if we can get the Europa League, we will take it with both hands."
Having replaced Andre Villas-Boas in December, Sherwood has brought stability to White Hart Lane and the comeback against Dnipro could now act as a catalyst to cement his position as head coach in the longer term.
He signed an initial 18-month contract but is having to deal with constant speculation he will be replaced in the summer by the likes of Frank de Boer or Louis van Gaal.
But Dembele is happy working under Sherwood and insists the whole squad is behind the 45-year-old.
"Would I like him to stay long term? That's not for me to decide," Dembele added.
"But how it looks now I think the team has confidence, we're playing much better and of course everybody is happy. After that the club has to decide, but as a team I think right now we are very happy."
Following the defeat at former club Norwich, Sherwood is keen to use the Dnipro result as a springboard for improved Premier League form.
"It is a big platform for us," he said.
"On the back of a poor game at Norwich we should be bouncing into the game against Cardiff. You are only as good as your last game and on Thursday we were very good.
"It will be a tough game. (Cardiff) are fighting for their lives and are bottom of the league.
"They have some maverick players who on their day can win games so we will be cautious of them but buoyed at the same time by the performance )against Dnipro). We should win that game."