Sagna spent seven years at Arsenal, signing three seasons after the club's final Premier League title win.
Sagna told the Gunners' In Lockdown Podcast: "We just played game by game and we were winning a lot but obviously and eventually when we had to perform in certain games, we were failing.
"Maybe it was because we put too much pressure on ourselves.
"Most of the games we had to play, we played well and we won. But for example when we had to play against the top four, we found it difficult to play against them at that time."
"I believe we under-evaluated ourselves. Playing for Chelsea image-wise was something different," Sagna added.
"They used their image a lot, they used to have some big players in the national team and we used to talk about them more than they talked about us.
"Maybe in our heads, they were bigger players than us. On the pitch, we had as much quality as they had whenever we played, and when we played the Arsenal way nobody could beat us.
"I believed nobody could beat us. We used to play simple passes, one, two-touches maximum. But I believe we under-evaluated ourselves which is a big mistake in life."