Holding a 2-1 first-leg advantage, Bayern fell behind three times on the night in the first half as record 15-time champions Real produced a familiarly strong performance on the European stage.
The tie was level at 4-4 on aggregate when Diaz struck in the 89th minute to put Bayern in front, before Michael Olise added another in stoppage time.
Bayern will face holders Paris Saint-Germain in the semis after winning 4-3 on the night and 6-4 on aggregate.
“I think even in the last 20 minutes of the game I felt like we were the team trying to make something happen,” Kane told reporters.
“They started to tire a little bit, and it just sometimes takes a moment, a moment of magic, an unbelievable finish, or an unbelievable pass.
“In this case it was two great finishes by Lucho (Diaz) and Michael (Olise), to finish the game off for us, and that’s what the Champions League is about.
“Sometimes, you can be the dominant team and lose, so it’s nice to get through and win this one.”
The England captain credited his side’s patience for helping them overcome Madrid.
“The highs and lows throughout the first half especially was pretty unique,” Kane said.
“We stayed in the game, we stayed patient, especially in the second half, we knew as the game would go on we would become stronger.
“Physically this season we’ve been really strong in the last 10-15 minutes, and that’s kind of what happened today. We took our chances when we needed to at the end.”
Kane’s first-half strike made him the first English player in a top-five European league since 1930-31 to score 50 goals in all competitions in a season.
“It’s a reward for a lot of the hard work that we put in, not just me, but the team,” Kane told TNT.
“It wouldn’t be possible without the players around me and for me it’s just about keeping it going.
“We’ve still got six weeks left in a Bayern shirt, we (England) have a World Cup in the summer and I just want to stay physically fit and sharp and just be out there to help the team.”
Bayern coach Vincent Kompany said his side were ready to take on PSG.
“We believe in ourselves more than ever,” Kompany said.
“We believed until the very end, never giving up after two tough battles against a great Real Madrid.”
Author
World Cup News
-
FIFA World Cup
/ 3 days agoCourtois ‘proud’ as sun sets on Belgium’s ‘Golden Generation’
Thibaut Courtois said he was proud of Belgium's fabled "Golden Generation" on Friday as...
By AFP -
FIFA World Cup
/ 3 days agoSpain vs France a World Cup ‘final before the final’: De la Fuente
Spain coach Luis de la Fuente said on Friday that the World Cup semi-final...
By AFP -
FIFA World Cup
/ 4 days agoMbappe warns ‘a long way to go’ for France at World Cup after reaching semis
France captain Kylian Mbappe insisted Thursday his team were not getting carried away about...
By AFP -
FIFA World Cup
/ 4 days agoDeschamps hails Mbappe after superstar fires France into World Cup semis
France coach Didier Deschamps paid tribute to forward Kylian Mbappe after he scored his...
By AFP