Morgan put Leicester ahead on the night to level the scores at 2-2 on aggregate before Marc Albrighton smashed home from the edge of the box to secure another famous victory for the Premier League champions.
Kasper Schmeichel saved Steven N'Zonzi's penalty after Samir Nasri was sent off for Sevilla and Morgan said Leicester are continuing to prove their critics wrong.
"Incredible, I can't quite believe it. We didn't expect to get this far and here we are," Morgan told BT Sport.
"It must be [the greatest night in the club's history]. I'm not sure it'll ever happen again but we did it, we proved a lot of people wrong. We pulled off the impossible again."
Get. In. You. Beauty.— Gary Lineker (@GaryLineker) March 14, 2017
There was an element of luck about Morgan's goal as Riyad Mahrez's free-kick bounced in off him at the back post but the centre-back has insisted Leicester will not get carried away with their success, having won their third straight game under new manager Craig Shakespeare.
"I just bundled it in," said Morgan. "I was in the right place at the right time and just happy it went over the line.
"We'll take whoever comes. We'll enjoy this moment, dust ourselves down and we've still got to concentrate on the league."
"I'm lost for words. What a night," Albrighton told BT Sport. "We thoroughly deserved the victory, we pressed them from the first minute to the last.
"We rode our luck but defended triumphantly and to get two goals against such a good team and keep a clean sheet is fantastic for us.
"We thoroughly deserve to be there, we've played brilliantly in this campaign. The Champions League run has been fantastic and we want to keep it going as long as possible."