The hosts had led through Grant Holt's early penalty, but found themselves trailing when George Friend equalised before half-time and then Grant Leadbitter put the Teessiders ahead inside the final 15 minutes.
However, substitute Jordi Gomez stepped up with just five minutes remaining to slot home a free-kick and make it 2-2.
Mowbray said: "From my point of view, we have a disappointed dressing room because we thought we had done enough to win the game.
"We worked their goalkeeper a lot more than they worked ours, and we are very disappointed we didn't win.
"We restricted them to a penalty that we gave them and a free-kick that my goalkeeper says is going straight to him and then takes a flick off someone on the way in.
"I suppose that was a by-product of the way we play. We got caught in possession and had to give away a foul on the edge of the box.
"It is a little bit deflated in there, but there are plenty of positives for us going forward.
"This was a difficult game but Wigan are a top side, who played in the Premier League last year, and who spent a lot of money in the summer."