Fletcher produced a bustling performance in the United engine room as the Premier League champions came from behind to beat Arsenal 2-1 at Old Trafford.
Wayne Rooney, who drew United level from the penalty spot, was named man of the match, but Ferguson felt Fletcher was deserving of the accolade.
"I think he was outstanding," Ferguson told Sky Sports. "It was a marvellous performance.
"He always does well on these occasions, he's a big game player.
"Rooney was fantastic in the second half and got man of the match, but I would have given it to Darren Fletcher."
The Scotland international appeared fortunate not to concede a penalty following a challenge on Arshavin moments before Arsenal opened the scoring.
However, Ferguson believes Fletcher timed his tackle to perfection and backed referee Mike Dean's decision not to award a penalty.
He added: "No, I didn't think it was a penalty, Fletcher clearly got the ball.
"The referee was 10 yards away and it was never a penalty kick.
"It was a committed challenge from Darren Fletcher and if he's late it's a penalty kick, but he got the ball."
United dropped four points against the Gunners last season and Ferguson was satisfied to secure a win in the first meeting with a fellow 'big four' club.
Ferguson continued: "When you are 1-0 down at half-time, it's always an uphill task against a team of Arsenal's capabilities and we had to dig deep.
"Winning the big games is important. Last season we lost four points to Arsenal, so we've got off to a better start against the bigger teams."