It is the first time that Spurs have reached the last eight for the first time since 2011.
Harry Kane's unerring finish completed Tottenham's safe passage to their second-ever UEFA Champions League quarter-final.
He said: "It is so important to be in the quarter-final, but you need to show more if you want to be at the next level".
The England striker became Spurs' all-time leading scorer in Europe with 24 goals.
Spurs fans were well aware of the contribution their experienced defender made in the victory, and were quick to praise him after the final whistle went in Germany, with many of them highlighting not just his performance on the evening, but his worth to their side overall.
Tottenham goalkeeper Lloris added: "As expected they pushed in the first 20 mins and we stayed strong together and that's why we got through".
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"It's been a very particular season with a lot of circumstance, so to be in the quarter-final is a fantastic, I think this will be one to remember. We scored four goals, did not concede and this was against a team that is top of the Bundesliga with great players", said Pochettino, who was yesterday banned for two domestic matches and fined £10,000 (S$17,850) for confronting referee Mike Dean after the Premier League loss at Burnley last month.
Speaking after the game, Burki said: "We knew it will be really hard because of the loss in the first leg. Tottenham waited for their chance and with Harry Kane up front you can do that. Now we have to deliver in the next few weeks, it starts on Saturday".
"We fully deserved this".
Dortmund flew out of the traps, pounding the Spurs defence with 10 attempts in the first half alone, restricting the Londoners to a single Son Heung-min effort, and enjoying 70 percent possession.