Television footage emerged of United wing-back Young appearing to elbow Tadic in the stomach as the hosts prepared to defend a corner in the second half of the Premier League clash at Old Trafford.
Young, 32, was charged by the Football Association with violent conduct and has since accepted a three-match ban.
Saints midfielder Tadic, who made little of the matter on the field at the time, gave his version of events to reporters after the game.
The Serbian said: “Yes, he elbowed me and I asked him, ‘Why did you do this?’. I didn’t really understand. I can fall down but it was really strange because I didn’t expect that from him.”
Tadic says he did not provoke Young.
“No, no, no, nothing,” said the 29-year-old. “I was surprised, and then next corner I asked him, ‘Why did you do that?’, and he said, ‘I didn’t do anything’.
“I said, ‘You didn’t do anything? You elbowed me in the stomach without reason’.
“OK, if you want to push it’s different, but an elbow is different.”
The incident was not spotted by referee Craig Pawson.
Asked if Young should have have been sent off, Tadic said: “Yes, but normally you cannot see that.
“I’m disappointed about that because you don’t expect that from him, because he’s an experienced player and he cannot do that I think.”
Southampton have not won in eight matches but the result was still an encouraging one after their 5-2 thrashing by Tottenham on Boxing Day.
“We showed great character and in some moments we could have taken three points, but we are happy to get a point against such a good team,” said Tadic.
The game was also Southampton’s first since it was announced defender Virgil van Dijk would be joining Liverpool for £75m in January.
Tadic hopes that money will now be reinvested in the squad. “I hope so,” he said. “I think the club will do that. We will see.”