“I spent my summer vacation convincing players to come, but when I come back the reality of the situation is there and we can’t keep up,” Rodgers said on Thursday.
“I don’t deal with the finances of the club. I run the football department and if they say we can’t sign a player, I trust the club, it is.”
Long-serving Foxes captain Kasper Schmeichel joined Nice earlier this month and other key players could yet leave with Wesley Fofana a Chelsea top target, while Newcastle had offers for James Maddison turned down.
After just one point from their first two games, Leicester are desperate for a win when they visit Southampton on Saturday to lift their spirits around the King Power ahead of a tough run of games that includes trips to Chelsea and Tottenham over the next five games.
Fixtures (all times GMT)
Tottenham v Wolves (1130), Leicester v Southampton, Crystal Palace v Aston Villa, Everton v Nottingham Forest, Fulham v Brentford (all 1400), Bournemouth v Arsenal (1630)
Leeds v Chelsea, West Ham v Brighton (both 1300), Newcastle v Manchester City (1530)
Manchester United v Liverpool (1900)