The defeat at Goodison Park was the first time they had not managed to win their opening fixture since 2008 and it's some eight years since they were beaten first time out.
United were just totally off form, they failed to create any clear-cut chances, even when new £24million man Robin van Persie came on in the second half.
Manager Sir Alex Ferguson was unhappy with their lack of a cutting edge and the big Serb agreed with him.
"We had some possession but we weren't clinical," Vidic told MUTV.
"When you go away from home you expect the home side to have some chances but we need to be more clinical.
"It wasn't a great game but we're already looking forward to the next one.
"We've lost our first match in the past and finished well so hopefully we can win our next game and go on a long run."
"We knew it would be a hard game," he added.
"They did what they're best at - playing long balls and focusing on set-pieces.
"They had a few chances and in the end deserved to score but we're never happy when we concede from a set-piece.
"Towards the end of the game Everton looked a bit tired and I believed, even up until the last minute, we would score because we had some good possession and they sat back a bit.
"Unfortunately we just couldn't get the goal."