On a night when victory would have seen the hosts swap places with Boro and move out of the drop zone with a win, Town lacked conviction and fluency in their offensive play.
The Teessiders dominated in the second half, but lacked a clinical edge with Ashley Fletcher producing a contender for miss of the season after firing over with the goal at his mercy early in the second half.
It was a night which was notable for two young goalkeepers being handed their league debuts with Ryan Schofield replacing the ill Kamil Grabara and Aynsley Pears, son of Boro legend Steve, stepping in for Darren Randolph, who had a thigh injury.
Cowley revealed that several of his players had been struggling with sickness ahead of the game with Boro - and they will be monitored ahead of Saturday's Yorkshire derby with Barnsley.
The Town chief said: "The overriding positive for us is that we picked up another clean sheet and are now five unbeaten with clean sheets in three of our last four games.
"And if you don't play well, don't get beat and I don't think we played well. Credit to Middlesbrough, they came and set up and pressed us aggressively and we could not beat their press.
"We were not able to get our counter-attacks off and were too slow in the speed of our play. I don't think we carried anywhere near the offensive threat we would have liked to offer. I did not think we played with any rhythm or fluency.
"We fought hard, but it was not an easy preparation for us. We obviously had the sickness bug which we had last week. It took out Karlan (Grant) last week and Adama hasn't trained. Kamil or Alex Pritchard didn't make it and a few others were under the weather and that is not giving players excuses.
"I try not to do that as they are good at doing that themselves."
Boro manager Jonathan Woodgate professed to a sense of frustration after seeing his side dominate in the second half, but fail to come up with a winner.
He said: "We had the best chances of the game and I thought we controlled the game in how we pressed. We deserved to win, to be honest.
"You have seen that in the last two games, we are creating chances to score goals. It is a big thing for me and I thought the performance was very good."
On the issue with Randolph and dropping top-scorer Britt Assombalonga to the bench, he added: "Darren has got a thigh strain, I am not sure how long he is going to be out for. Aynsley did not have much to do, but what he did do, he did well. His concentration levels for a young goalkeeper were terrific.
"Britt has played every single minute and I just thought I would take him out of the firing line. The plan was more or less to give Britt twenty or thirty minutes."