Goals from Raheem Sterling and Kai Havertz sealed the Blues progress with a 2-1 aggregate triumph.
That comes after the Blues’ wretched recent run was snapped with a 1-0 Premier League win over Leeds United.
“I think the supporters have been really fair with us,” Potter told reporters. “Supporters care, so when the results aren’t what they want, they feel pain.
“They have to articulate that pain somehow, to get rid of it, and whether that’s at me or whoever it is, we all know in this job that is what happens. They’ve been really supportive, they really have. They’ve stuck with the team and helped us on the pitch.
“Rightly so, when we haven’t performed the way we should, they’ve let their feelings known and that’s fair enough.
“You always need a bit of luck, as much as we think we’re these talented coaches and talented players.
“I would say before the World Cup, we had nine players out. If you have no Reece James, no N’Golo Kante, no Wesley Fofana, no Ben Chilwell, no Loftus-Cheek, no Sterling these players are important for us as well.
“Tonight they had some players missing and that goes in our favour. I’m not going to complain about that at all.”
Potter declined to label the match “make or break” when asked if that’s how he felt going in amid intense pressure.
“I don’t really think about it in that way,” Potter said. “There are always going to be those types of questions and noise.
“My job is to help the team, help the players, prepare the team as well as we could and to support them. They’ve been suffering as well. Nobody has enjoyed the run we’ve had. That’s why today was important for us. We wanted to progress, and we have, so we’re happy.”