It was a second successive game at the Riverside where Boro had dominated and squandered chances and had to battle for a draw.
Wednesday went ahead as Michail Antonio hooked home from a corner just before the break and Boro levelled soon after the restart through Mustapha Carayol - but they created enough chances to win.
Mowbray rued his side's lack of clinical finishing and said: "Wednesday came with a game plan to go on the counter-attack.There were times they pressed forward and that gave us space to play.
"It was different from Blackpool who banked up and got everyone behind the ball. Wednesday gave us a bit of room to play, but we were far from dynamic.
"We need to learn how to break teams down and finish them off.
"We had a lot of great chances, but need to start taking them."
"And we gave them too many corners and they punished us. They were like the land of the giants in the box - although for the goal we had four defenders stood near the ball and their lad reacted quickest."
Mowbray still hopes to bring in reinforcements before the transfer deadline.
He said: "Everybody is working hard to put things in places to get somebody in.
"I would prefer a permanent signing rather than a loan. We are trying to build a team and I think the team is starting to take shape and look like one that we coach."
Wednesday manager Dave Jones thought his side may have had more than just the single point.
"I thought we shaded the first half and they shaded the second, but we had two great chances near the end," he said.
"We had a right go at each other at times and we were two quick sides who tried to play it the right way.
"I can't fault my players. They looked bright and sharp and could have won it.
"But Middlesbrough scored when we had a spell where we gave the ball away too cheaply.
"We might have got away with it two years ago in League One but you don't get away with it at this level."