Rodgers allowed Carroll to leave on Thursday night thinking
However, Liverpool failed to match Fulham's demands for
It has left Liverpool chronically short of strikers.
Rodgers did not have an orthodox forward on the bench for his side's 2-0 home defeat by Arsenal and is now left to consider moves for the likes of
"No," said Rodgers when asked whether he would have let Carroll leave, then 'very' when quizzed about how confident he was of getting in a replacement.
And for the likes of Owen and Drogba?
"I can't say no. Any player I believe can improve the squad, I will look at," he said.
"We have a very small group. We had 19 training yesterday. It is something that would have to be discussed."
The result condemned Liverpool to its worst start to a season since 1962-1963.
It was hardly the best way to mark Bill Shankly's 99th birthday, although Rodgers tried to put on a brave face.
"I am not here to cry," he said.
"Whatever has happened, I wouldn't change it for the world.
"I am very proud to manage this club. I have made it my life.
"I felt we needed reinforcements. That is the reality. But it is gone now. The window is shut.
"We have to concentrate on the players who are already here."
Rodgers spoke with the Liverpool hierarchy about what went wrong, but he is refusing to pin any blame on owner
"There is no doubt the finances here had to be changed," he said. "That was the reality.
"We have lost nine players and brought in three. From a business side the club has done well.
"What we have to do in the future is look after the football side.
"Hopefully in the next window - and the ones after - we can transition a group that allows us to compete.
"But it is a learning process for the owners as well. They invested £100 million ($154.22 million) into the club and then changed one of the most iconic figures at the club.
"They made a big commitment to have me here for the longer term and have been very up front with me.
"There are one or two things we need to iron out. If we do that it will help us in the next window and the ones after. But they have not misled me."
The sucker punch duly arrived when
Liverpool briefly threatened a reply after half-time, but ran out of ideas and the excellent Cazorla profited from
"Everybody understood quickly Cazorla would not need six months to settle," said Gunners boss Arsene Wenger.
Wenger also confirmed he was hopeful
"Jack is looking very good in training. We will give him a month. Then he should start to play," he said.
English Premier League
Brazilian midfielder Fernandinho has confirmed he wants to join Manchester City.