Cucurella struck from 25 yards on the hour mark as Chelsea won 1-0 on the day.
He told Sky Sports: "We know that we need to defend with everything and today the team showed a lot of passion.
"I think Enzo passed me the ball and I see that I have the option to shoot. Normally I wouldn't but I tried. We got the three points and we want to fight for the objectives.
"I'm really happy. I think it's a long process, I needed to work really hard in my bad moments. Maybe something I need to improve is being more clinical in the final third.
"In the last minute we showed energy and the fans helped us in our tough moments when we're a bit tired. We defend the same club and we need to stay together. The support is very important when things go not well."
Blues teammate Jadon Sancho also stated: "It was a much-needed win, we knew Leicester would come here and give it their all. We stuck to the game plan and we got the three points.
We had a lot of chances, we should have converted more goals. That's football, you score some and you lose some.
"He (Cucurella) does that in training quite often so I'm not surprised. We want to win every game.
"Next two games; Copenhagen on Thursday and then Arsenal. We have to be prepared."