The hosts looked down and out when Leicester's former Boro striker Ayegbeni Yakubu completed a hat-trick early in the second half.
But, in a frantic finale, they clawed a goal back then missed a penalty and twice clipped a post before Stephen McManus headed an equaliser deep in stoppage time.
"We were delighted with the comeback," Mowbray said. "In the end we are even a bit disappointed that we didn't win it because once we got to grips with the game in the second half we created the better of the chances.
"We missed from the spot and we hit the woodwork twice and so we could maybe have got the win but I don't think anyone could deny that we deserved at least a draw."
Source: PA
Source: PA