Wigan Athletic said in a statement: "We cannot issue duplicate tickets because it opens the club to fraud.
"The club is carrying out a full investigation. It doesn't want to let the fans down. TNT says it is also carrying out its own investigation.
"The club can only apologise and promise the fans that we will be looking into the reasons as to why this has happened."
'Desperate' situation
The statement added: "The club is currently contacting the supporters to explain the situation but regrets that this happened and really does sympathise, but has done everything possible to avoid this situation occurring."
TNT were unavailable for comment.
Greater Manchester Police (GMP) doubled the number of officers they usually provide on match days as they were expecting a larger crowd.
There were fears ticketless United fans could travel to the match ready to celebrate if they win the league title.
Outside the stadium, the Wigan fans without tickets said the situation was "desperate".
One said: "We've come to the ground, the ticket office said (the tickets) had been sent out but they haven't turned up."