United stuttered to a 1-1 home draw against Southampton on Saturday to leave the reigning champions eight points adrift of Premier League leaders Arsenal and only four above the relegation zone.
Moyes was handpicked by Ferguson as his successor in the summer as the veteran manager called time on a 26-and-half-year reign at Old Trafford and his team have begun the new campaign in lacklustre fashion with one win in four home league games.
Some critics have suggested visiting players now head to Old Trafford confident of upsetting the hosts, but Moyes said: "I think the fear factor is from the team on the pitch, that's always the case.
"The players are the thing because of their quality. Obviously Sir Alex has a great history and there is all his experience but the players will always be what matters on the pitch."
Despite the early wobbles for Moyes since moving from Everton, Ferguson has insisted that winning any trophy in his first season would be a creditable performance.
It took Ferguson nearly four years following his arrival at Old Trafford from Aberdeen to win his first silverware, with the 1990 FA Cup success giving him the breathing space he needed to set the club on the path to 13 English League titles and two Champions League triumphs.
"For David, winning a trophy would be a fantastic achievement," Ferguson told MUTV.
"No matter what it is - the League Cup, FA Cup, European Cup or Premier League. It is not easy winning a trophy in our league because you could say there are six teams fighting for the league."
Ferguson was in the stands on Saturday and would have been frustrated to see Adam Lallana scramble in Southampton's equaliser in the 89th minute to cancel out Robin van Persie's early strike.
And Moyes was upset at the inability of his players to kill off the game having led for so long.
"It's disappointing because we wanted to get a bit of momentum going and we weren't able to do that," the Scot added.
"We didn't do well enough defensively. We work on that in training but we should probably have put the game to bed earlier on. But we've got to do better at set-pieces, make sure we defend it and make sure we're harder to score against than we were."