Divock Origi showed glimpses of the potential that convinced Liverpool to splash out on him after the 2014 World Cup, but was guilty of missing several chances.
Rodgers added: "We had a number of chances and you've got to be clinical. They were real good chances and unless you score them you won't win at this level.
"Give credit to them, they worked hard and defended well but we're disappointed because we have to win a game like that."
On Origi's performance, he said: "I thought Divock did well; all that was missing was a goal and he'll be disappointed as he needs to add that to his game over the years."
Reds' goalscorer Adam Lallana added: "It was important for us to win. We had enough chances to win but we're disappointed - we wanted the three points and we felt we created enough but it wasn't to be.
"We have to move on quickly for a big game on Sunday against Everton."
