The Reds found themselves 2-0 down within 32 minutes courtesy of goals from Morgan Schneiderlin and Rickie Lambert and, despite pulling one back before the break, it was a deficit that they couldn't overturn.
"We just weren't very good. It was as simple as that. If you start a game the way we started it then it is very difficult at this level to get back. We only started to play when we were 2-0 down. We got it back to 2-1 and we were better in the second half but then conceded another very poor goal," said Rodgers.
"Today was a poor day at the office. The problem is we have to live with it for a couple of weeks now. When you concede the goals we conceded today it is always going to be difficult to win games.
"It's something I know that we need to improve. We need to develop as a group. Today we didn't defend or play as well as we can. I know the areas where we can improve."
The result leaves Liverpool seventh in the Premier League table, five points off fifth-placed Arsenal.