The Packers' troubles deepened in an upset defeat to NFC North rivals the Detroit Lions, who triumphed 15-9 on Sunday.
Green Bay had not lost five on the bounce since 2008 – Rodgers' first year as a starter – but they are a team devoid of confidence at present.
Rodgers' own display summed up the fortunes of his team as he threw three interceptions in a game for only the fifth time in his career and for the first time against NFC North opponents.
Two of those came with the game still scoreless, giving the lowly Lions a foothold they fought hard to protect.
"I had some s***** throws, for sure," said Rodgers. "I played s*****, but I never gave up.
"We moved the ball well in the first half, and I threw a couple picks in the end zone, took points off the board. That, obviously, came back to hurt us down the stretch.
"I've been counted out many times in my life as have many of my team-mates, and I hope we just dig deep and find a way.
"We will truly be underdogs for many games moving forward. Hopefully we can embrace that. We have two games at home. We've got to go win those two games in a week, and then this thing looks a little different."
Packers coach Matt LaFleur conceded the going was tough but wants to see Rodgers and his team-mates channel their frustration more productively.
"I'm sure he's extremely frustrated, as we all are," LaFleur said.
"I don't think we've been in this [situation]. I know in my time here, we haven't been in this situation and I don't think he's been in this situation too many times in his career, obviously.
"It's disappointing and frustrating. But I think that we all probably need to do a little bit better job of controlling that frustration."