The Red Devils dominated the vast majority of the last-16 second leg, but needed a 70th-minute goal from Mata and a string of second-half saves from Sergio Romero to seal their progress into the quarter-finals following a 1-1 draw in the reverse fixture.
Mata admitted that his side were once again not clinical enough in front of goal, but is pleased to have taken another step towards lifting the trophy for the first time in the club's history.
"It was a matter of finishing our chances again. We created some good chances but we could not score. It is important we kept a clean sheet so we are happy today," he told BT Sport.
"They are a team that push until the end. They play with a difficult system but we adapted well. We are playing at Old Trafford and need to do well.
"Our aim is to win every tournament we play in. It is a good chance to play Champions League next season and we will try until the end. The level in the Europa League is difficult."
The victory ensured that United maintain their 100% European home record this season.