Farhad Moshiri has claimed he retains faith in the under-pressure Frank Lampard and the under-fire Everton board despite the team’s descent into the relegation zone.

The Everton hierarchy had been silent on Lampard’s position after the calamitous 4-1 home defeat by Brighton last Tuesday but, responding to a letter from the Everton Fans’ Forum, the owner offered the manager some support and insisted the club needed stability. Moshiri also rejected growing calls from a wide range of Everton supporter groups to replace the chairman, Bill Kenwright, and other members of the club’s board.

“I have faith in the work being done not only by our manager, but our director of football [Kevin Thelwell] and our board of directors,” Moshiri wrote to the Fans’ Forum. “That faith is based on my knowledge of the depth and quality of work being done both at Finch Farm [Everton’s training complex] and the Royal Liver Building [Everton’s administrative HQ) – and of the plan that is in place. I am confident that we have skilled, experienced and focused professionals at all levels of the club. We are all agreed that our current league position must and will improve.”

Lampard said last week that he did not want or need a vote of confidence from the Everton hierarchy, although the manager accepts he is in a precarious position following a run of nine defeats in 12 games. Moshiri has previous form for publicly backing a manager shortly before sacking them and has dismissed five during a turbulent seven years in charge.

Everton host bottom-of-the-table Southampton on Saturday in what appears a critical game for Lampard and his team’s latest relegation struggle. Everton’s last match at Goodison Park, the loss to Brighton, saw chants of “sack the board” echo around the stadium. There were similar protests during the FA Cup defeat at Manchester United on Friday and a sit-in demonstration is being organised for after Saturday’s game by the #AllTogetherNow campaign.

The campaign, comprising numerous fan and social media groups plus 21 official supporter clubs, is calling on Moshiri to “make sweeping changes at chair, board and executive levels. It demands he brings in competent, experienced professionals who can reverse the club’s decline, and make the necessary changes to make Everton competitive once more.” The Everton Shareholders’ Association also issued a statement on Wednesday, saying it is in dialogue with Moshiri. “Our views are consistent with those of other groups who want positive change that will bring about a better Everton Football Club,” read the statement.

However, Everton’s owner has claimed that a restructure at the top of a club facing another fight for Premier League survival is not on his agenda. Moshiri adds: “In almost seven years since my arrival at the club, I have significantly increased my investment and our new stadium has become reality.

“We regularly review our performance and initiate change where we feel that the club falls short of standard. This has meant that we have seen turnover in managers, directors of football and several board members, but always as we have striven to achieve success. Whilst, in virtually every instance, change has been supported and encouraged by fans, stability must be the key to progression.”

Meanwhile, the Football Association has announced it can charge clubs if their fans are caught singing the “Chelsea rent boy” chant.

The chant has been heard at Chelsea’s recent matches against Nottingham Forest and Manchester City, and also at Everton’s match at Old Trafford on Friday, when it was aimed at Lampard, a former Chelsea player and manager.

While the FA has always condemned the use of the term, it has never felt able to charge clubs over its use. However, it is understood the recent conviction of the Liverpool fan Paul Boardman, who admitted using the term on his way to last season’s FA Cup final against Chelsea at Wembley, was a gamechanger, and opens the door for the FA to punish clubs where fans are proven to have used the term.

An FA statement said: “Today, the FA has formally written to all clubs across the Premier League, EFL, National League, Women’s Super League, Women’s Championship and Steps 2-4, to remind them that it can pursue formal disciplinary action against any club whose supporters engage in discriminatory behaviour, now including the use of the term ‘rent boy’. The FA has now informed all clubs that it considers the ‘rent boy’ chant to be a breach of the FA rules.”