City appeared to be on course to win in regulation time when they still held a 1-0 lead courtesy of Bernardo Silva heading into stoppage time, but Leicester were then awarded a controversial penalty – Kyle Walker judged to have fouled Demarai Gray.
Vardy scored that penalty but, after things remained level throughout extra-time, the England striker saw his spot-kick in the shoot-out hit the outside of the post and then Riyad Mahrez had his effort swatted away by Claudio Bravo.
But Guardiola does not think City will be celebrating an unprecedented quadruple at the end of the season, with the club also still in the FA Cup and Champions League, as well as being runaway and undefeated leaders in the Premier League.
"Forget about it," Guardiola said to Sky Sports. "That’s not real. That's not going to happen, no."
The Catalan coach also suggested Leicester were lucky to have made it to a shoot-out in the first place, with Gray in his opinion fortunate to win the penalty that Vardy converted.
He added: "The TV doesn't lie. We can see if it's a penalty or not, but we overcame the situation. In football, sometimes these kind of things happen."
Midfielder Ilkay Gundogan – who brilliantly created Silva's opener – added City were "unfortunate" to have that decision go against them and hailed the reserves of mental strength in a youthful and experimental line-up.
What a jumpy and straining match against @lcfc. You get 8 minutes of added time and one very unfortunate penalty. For most teams it‘s really hard to get back on track. Guess we‘re not like most teams. #foxesvcity @ManCity pic.twitter.com/OYLOhWo2mo — Ilkay Gundogan (@IlkayGuendogan) December 19, 2017
"What a jumpy and straining match against Leicester," he wrote on his official Twitter account.
"You get eight minutes of added time and one very unfortunate penalty. For most teams it's really hard to get back on track. Guess we're not like most teams."