The Reds struggled to make any impression in a flat first half before recapturing some of the team’s recent domestic form after the interval to coast home with goals from Ashley Young and Javier Hernandez.
With the second leg to come at Old Trafford next Thursday, United must be strong favourites to progress to face Lokomotiv Moscow or Athletic Bilbao in the next round of the Europa League with the Russians 2-1 ahead after their first-leg tie.
“I’m delighted with the scoreline but I think it was a very ordinary performance by us,” conceded Sir Alex. “We didn’t reach any great heights in the game.
"We did improve in the second half and I thought we deserved to win it but I didn’t think we played well at all. There was no rhythm to our game. I know Ajax can make it difficult with their system and they pressed the ball really well but we didn’t get any tempo to our game in the first half. We did improve in the second half but it was not a brilliant performance."
The boss was asked whether United should complete the job and continue to progress in the competition.
“Absolutely, it gives us a good opportunity but we’re taking nothing for granted, of course. We’re at home at Old Trafford and we have a good opportunity to get through.”
Sir Alex felt Javier Hernandez was out of luck for most of the evening so he was delighted the Mexican finished clinically when put through by Wayne Rooney towards the end.