Leicester defended poorly and gave up possession too easily in another demoralising defeat that left them with a single point from their opening six games having lost their last five matches in a row, their worst start to a season since 1983-84.
Next up is a home match against Aston Villa.
"You can only work hard," Rodgers told BBC Sport. "We need to pick the players up for another home game next week, which will be a big opportunity for us. If we can sustain the game for longer and not make mistakes, we can build towards getting a result."
The defeat will put Rodgers’ position in the spotlight and he accepted blame for their plight.
"My focus is on the football and trying to give the players the confidence and structure to our game to get back to winning," he said. "We will arrive with a new energy, focus and hopefully confidence into the game next week.
"You put the hard yards in now and work, not shirk responsibility. The results are down to me, I am the manager, and we need to go away and work even harder and get that first win."
Leicester could not retain the ball at Brighton, which Rodgers admits was not a one-off.
"It has been a problem for a while," he said. "The simplicity goes out of your game if you lack confidence and you stay on the ball longer than you should. At the moment it is not quite happening for us.
"In spells we look dangerous, but we don't conserve the ball long enough to sustain any period of the game."
