"They didn't want to play, they defended so deep and just wanted to counter-attack," Guardiola said after seeing a side he has managed concede five goals for the first time in his 686th game in charge.
"They scored the first time they arrived and had three penalties in total, so it was very difficult for us. The lack of creating chances made us nervous and anxious."
At the other end, they looked like conceding every time Leicester came forward, with Vardy's speed causing all sorts of problems.
The striker won both penalties he converted either side of a classy back-heel finish, while James Maddison added a fourth with a superb shot and Youri Tielemans put the icing on the cake with a late penalty.
Guardiola rued his team's lack of composure but vowed to bounce back after City conceded five goals in the league at home for the first time since a 5-1 defeat by Arsenal in February 2003.
"It's a tough result but I am not going to give up. I am going to find solutions for the team to be stable," he said.
"My players might have thought that they weren't playing well enough after conceding the equaliser but we were well on top at that stage.
"The problem was that we put extra pressure on ourselves to score the second and third. We need to be more calm, we don't have the players to attack the box that we need.
"We needed to be more patient. It is hard, but it is the second game of the season and we have to try to see what we need to do to avoid it from happening again. I feel bad for the guys and for the club."