Chelsea drew 1-1 with Leicester at Stamford Bridge despite an impressive start which saw them take an early lead.
Lampard’s men came out of the blocks fast despite playing extra-time against Liverpool in midweek, but failed to build on Mason Mount’s early goal.
Zouma, who was widely criticised for his performance in their 4-0 defeat against Manchester United the previous week, has now given his thoughts on what went wrong.
He said: “There is a long way to go and we are not worried.
“There are players who came back from loan – like me – and other players, the younger guys who came in.
“Now we are starting to understand each other. We just need to be more clinical. We just need to score more goals.
“We wanted to win the game but listen, I’d say we were maybe a bit tired in the legs. Obviously, Leicester played well.
“They pressed us very, very well and we had to deal with the pressure.”
Brendan Rodgers’ side had the better of the second-half in London and could’ve been considered unlucky not to leave with all three points.
Chelsea seemed to run out of steam late on despite the introduction of Tammy Abraham, Willian and Mateo Kovacic, as Jamie Vardy and James Maddison missed good chances to score a winner.
Zouma added: “We were tired. We tried to press but we didn’t have the legs so maybe we have to stay more back, control the game a bit more, try to keep the ball a bit better. But these are the things we learn.”
The 24-year-old has also given his take on if the UEFA Super Cup should skipped extra-time and gone straight to penalties, but he remained impartial.
He continued: “I don’t know if UEFA were wrong to ask clubs to play extra-time. You should ask higher up.
“We had a long journey after the game and played 120 minutes there so it was difficult. We need to work hard.
“We have to prepare for Norwich this weekend now. Every game, we must win. We want to win this one, of course.
“Myself, I knew I made mistakes in the first game but it won’t be perfect every game. You have to learn from games. I am still learning.
“After a game like this, you just have to refocus, keep the concentration high and then I think I did right after that by keeping myself ready and prepared.
“I’m not surprised I’ve played every game because that’s what I wanted. I came here and wanted to play. I am in a big club and everyone here wants to play. The competition is very hard.
“You always have to look over your shoulder. The squad is very talented and the competition can only make us better.
“Today I play, tomorrow maybe not but I want to play every game. Everyone that’s on the pitch wants to stay on the pitch and we have to work hard for that.”