With the sides level at 1-1, Deadman awarded Bolton a penalty on 58 minutes when he adjudged that Jonathan Woodgate had taken down Chung-yong Lee.
Deadman then dismissed Woodgate six minutes later for a professional foul on Marvin Sordell, and Mowbray was unhappy with both decisions.
He said: "I thought we deserved more than that and we needed a better official to referee the game because there were some bewildering decisions out there today.
"The penalty was one of them and the sending-off was certainly one of them."
Chris Eagles put Bolton ahead on 50 minutes and although Boro mustered a quick reply through Keiron Dyer, Sordell's spot kick consigned them to defeat.
Mowbray said: "Bolton started the game well, which they always do but I thought we had a decent foothold in the game and then they got a goal through a cross which just drifted in, but that's the way our luck has been going at the minute.
"I thought we were the better team but the history books will show that we lost.
"They won't show that we conceded a lucky goal and then a penalty, which having seen half a dozen times was never a penalty kick, but that sums up the referee's performance."