However, Pochettino, 47, is far from happy with having a day less to prepare for the last 16 tie at Dortmund's Signal Iduna Park.
But the hosts found it hard to break them down, and when they did, they were met by an imperious Hugo Lloris who seemed impenetrable in goal.
Pochettino said, "We are in the quarter-finals".
"It's massive for momentum after a tough week in the Premier League we had", was Kane's summation of the win when he spoke to RTÉ Sport afterwards.
DF Serge Aurier, 7 - Most of Dortmund's most risky attacks came down his side in the first half, but he played his part in the clean sheet and put in a good late cross towards Erik Lamela.
"I don't know if the FA or the Premier League are to blame or television, who wanted us to play live Saturday or Sunday". They cancelled their game at the weekend to help Rennes to play against Arsenal.
"I expect to play at the new stadium". In [other countries] it's more sensitive - the FAs help the clubs to compete in the best way in Europe. We need to feel proud.
The coach had to leave a key member of the squad back in London
"We need to show the same aggressiveness, play our way".
Roma won the first leg at home, 2-1, but could be kicking themselves after allowing a crucial away goal late in the match.
Harry Kane is expected to lead Spurs' attack while Pochettino said Harry Winks and Eric Dier could feature after injuries.
The only consolation for Dortmund is that they can now exclusively focus on the winning the Bundesliga, with their lead at the top recently slipping, as Bayern Munich are now level with Die Schwarzgelben with only ten games of the season remaining, having had a nine-point lead after 15 games.
Nicholas added: "Dortmund were the better team at Wembley in the first half but ended up losing 3-0 so we know how quickly this can turn - I think Spurs need a goal to get through, and I think they will because there's a goal in them".
"We were sitting and listening to the Champions League song and we were talking with Jesus (Perez, Pochettino's assistant) saying it will be incredible to be in the new stadium listening to that song before the game".
"Now it's about enjoying that we are in the quarter-final".More news: Jurgen Klopp issues injury update on Roberto Firmino