David Moyes faces a fight to convince several senior Manchester United players of his credentials following the dismal form that has resulted in three consecutive defeats for the first time in 13 years.

The Guardian can reveal that some within the dressing room are unsure of Moyes's ability to reverse a sequence that includes a league defeat by Tottenham Hotspur, being knocked out of the FA Cup by Swansea City, and Tuesday's 2-1 loss at Sunderland in the League Cup semi-final, first leg.

The Football Association, in addition, is looking into Moyes's remark after the tie at Sunderland that we are "playing referees as well as the opposition". The manager could face a charge if it is viewed he was commenting on match officials' fairness.

When Moyes was appointed as Sir Alex Ferguson's successor at the close of last season he brought in his own coaches – Steve Round, Phil Neville, Chris Woods, and Jimmy Lumsden, and also appointed Ryan Giggs – while discarding the existing backroom staff of René Meulensteen, Mike Phelan and Eric Steele.

This move is being privately questioned by some within the squad who were happy working with a group that had helped Ferguson oversee part of the most successful period in United's history. According to well-placed sources, there is a bemusement among a number of players, with a strong sense forming that as United won the title by 11 points last term there was little need for Moyes to undergo a complete revamp of a set-up that had a proven winning structure.

Moyes has never won a major trophy as a manager and, for some, his record is now under scrutiny, given the team are 11 points behind the leaders, Arsenal, and have scant chance of retaining the title. There is further concern that United may fail to qualify for the Champions League for the first time since 1995-96, with the side in seventh position, five points behind fourth-placed Liverpool.

While there is no sense of a player mutiny at present, this week's revelation that the club captain, Nemanja Vidic, is exploring leaving this summer, despite United wishing to open discussions over a new deal, is the latest crack in unity.

Before the defeat at Sunderland, in which Vidic scored United's equaliser, his agent, Silvano Martina, told an Italian radio station: "At the moment, I would rule out an extension [to his contract] with Manchester United."

Vidic's disquiet follows Danny Welbeck's denial of the claim last month by Moyes that the manager had to instruct the striker to be "the last off the training field" in order to improve. Within days the player offered a counter-view. "I have been doing that [extra training] ever since I have been at United," he said.

Earlier in December Rio Ferdinand publicly questioned Moyes's policy of naming the team close to a match, rather than the day before, as Ferguson did, stating it could turn the defender "into a madman".

Moyes's pursuit of Leighton Baines to replace Patrice Evra has not gone down well either, given the left-back's popularity in the dressing room. As with Vidic, the Frenchman may consider his options as he is out of contract in the summer.

All of this means that following the loss of the three matches in seven days, some senior players who were serial winners have been left uncertain about the direction of the club under Moyes.

After the defeat at Sunderland Welbeck became the first to voice concern regarding prospects of qualifying for next season's Champions League. Asked if he could understand why supporters are worried United may finish outside of the top four, he said: "I can understand why fans are concerned. We are not around the Champions League spots at the moment. We need to get our form back and just win the next matches."

The striker is unsure why after clinching the title last season United are so far adrift of Arsenal. "I cannot pinpoint one thing why this is happening. We were champions last season and we know that the consistency in our game has not been good enough," said Welbeck. "It is a new experience for us all but the main thing we have to do is look at the next game."

He did state a determination to start winning games. "It is over 10 years since United lost three games in a row, so we know we have to turn it round and win the next match. The manager is very upbeat. He lets the players know he wants to do really well and the players also want to win games for United," he said. "Losing three on the bounce is really not good enough and we want to put that right."