Brendan Rodgers has told Liverpool's owner, Fenway Sports Group, the club needs to buy "some men" this summer to eradicate the lapses that have plagued his debut season at Anfield.

Missed opportunities and defensive errors again cost Liverpool on Thursday when losing 2-0 at Zenit St Petersburg in the Europa League, leading Rodgers to question the mentality of the squad and strengthen his calls for greater character. Ashley Williams, the Swansea City defender who will oppose Liverpool at Anfield on Sunday, is one such target for Rodgers, though he may have to convince FSG to sanction a move for a 28-year-old to prise the Wales captain from his former club.

Liverpool have failed to challenge for a top-four place this season and a Europa League exit to Zenit would end their prospects of a trophy. The manager believes it is the calibre of signing, not the quantity, that will instigate an improvement.

Rodgers said: "The biggest thing we need this summer is to bring in some men, some character that allows and supports the other men to see the games out. That is the biggest thing for me. Look at Jamie Carragher. He is our best defender, he is 35, but we are losing that character. That has to be replaced somehow.

"I also think there are other areas of the team that need improving. They have to be established players and they have to have that hunger, that is the key thing."

Liverpool's managing director, Ian Ayre, has denied that FSG has implemented a rigid policy of signing only young players under Rodgers, although the club have not bought anyone over 24 since he became manager. Liverpool paid £8.5m for 20-year-old Philippe Coutinho last month, after Rodgers admitted there was a need for experienced leaders, and doubts remain over the extent of the manager's influence on transfer policy.

He added: "That is something we will talk about at the end of the season, when we identify where the improvements have to be made. Personally, I just want the best team. Whether that is senior players, youth players, or the best, which is the mixture. I always like to give young players hope but in order to do that they need that bit of experience alongside them."

Rodgers insisted that Liverpool will not require "wholesale changes" this summer, citing the impact of the £12m January signing Daniel Sturridge as a lesson in "improving key areas if we are going to make the jumps we need to make.

"It is not something I'll talk about now," said the Liverpool manager. "Martin Skrtel came into the team against Zenit and did well. I gave him a new contract in the summer because I had faith in him. This has been a difficult but a real eye-opening period in terms of coming into a club with such ambition.". Yet with Carragher retiring, Liverpool open to offers for Sebastián Coates, and Skrtel out of favour, Rodgers could require three new signings in central defence alone.

"I don't think massive surgery is needed. Maybe if we had a few more of Daniel Sturridge's capacity in the group that could set us up. Technically we have shown we are very capable, tactically we have not been found wanting like in the recent two games against Arsenal and Man City. The condition and intensity of their work is high so that only leaves one thing – mentality.

"That is the area which needs to improve and to do that we need character."

Liverpool host Rodgers' former club Swansea in a re-arranged Premier League fixture on Sunday with Joe Allen, his £15m signing from the Liberty Stadium, admitting he is struggling to understand the first dip in form of his career.

The Wales international said: "I don't think it is a secret that I have not had my best spell in recent times. I haven't performed but I am working hard and striving to change that. I think it is the first time I have had to deal with a dip in form like this. These are things that you have to overcome. It probably takes a little longer than you would hope but it is down to myself. I am self-critical and that is why my form hasn't improved as quickly as I would have liked."