Madrid looked dead and buried as they trailed 2-1 deep into stoppage time in Trondheim, but Sergio Ramos' equaliser sent the match to extra-time where Dani Carvajal's brilliant 119th-minute goal won it for the European champions.
Zidane told a press conference: "In football you never know what's going to happen. The good thing about tonight is that we knew it was going to be difficult, but we never gave up.
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"They got ahead in a key part of the game, but we never gave up and Sergio's goal in the last minute brought us back to life."
Madrid, who were without the likes of Cristiano Ronaldo, Gareth Bale and Toni Kroos, had taken a 21st-minute lead through a superb goal from 20-year-old Marco Asensio but Sevilla were back on terms just before the break through Franco Vazquez.
Real Madrid players celebrate scoring against Sevilla in the European Super Cup
Image credit: Reuters
Sevilla went ahead with 18 minutes left when Yevhen Konoplyanka slotted home from the penalty spot after Vitolo had been tripped by Ramos.
That looked to have won Sevilla the title but Ramos made amends for his foul by heading home in stoppage time, and then full-back Carvajal proved an unlikely winn er with a last-gasp solo goal sealing a 3-2 victory.
Former Sevilla defender Ramos, who also scored a stoppage-time equaliser in the 2014 Champions League final against Atletico Madrid before his side went on to win 4-1 in extra-time, said on his club's website: "It's incredible.
"Until the final whistle goes you need to continue fighting because by fighting to the end you get your rewards.
"More than anything you need to highlight the collective work of the team and its fight. The team, despite the players missing, have shown what they are about here and to start the season with a title is always incredible."
New Sevilla coach Jorge Sampaoli, whose side lost Timothee Kolodziejczak to a red card in extra time, said: "I'm proud of the way we played.
"Without much time to work together this team showed courage against the champions of Europe."
The Europa League holders, who have now lost three Super Cups in succession, do not have much time to dwell on the loss as they play the first leg of the Spanish Supercup against Barcelona on Sunday.
"Tomorrow we will start to think about what comes next and help the players recover," added Sampaoli.
"These types of cups are quite prejudicial to your preparations (for the new season). We had to cut our preparations to arrive at this game. It will be a case of counting on those players who are 100 per cent."
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