Boro, who came into the game on the back of draws against Newcastle and Derby, went ahead through a Chris Killen header two minutes into the second half.
But Reading battled back to level after 63 minutes as Jimmy Kebe drilled in a low shot from a tight angle that deflected in off David Wheater at the near post.
"We are all very disappointed because it is a game we all know we could have won," said Cooper, facing the media in place of boss Gordon Strachan who had to rush off to a family commitment.
"We are three unbeaten but we haven't won a game either and if we are to have a chance to get into the play-off picture we have to start winning games.
"We worked hard enough as a team and we had a few little spells where we were on top and created chances but it wasn't to be. We huffed and puffed but to be honest we weren't good enough to win today.
"No-one is to blame for that. You can pull individuals to bits if you want but there just wasn't a spark there as a team.
"Both sides had chances but the game was a bit flat and we didn't do enough to rise above that."
Reading carved out the best chance of the first half after 30 minutes as Jobi McAnuff wriggled into the box from the left then chipped towards the far post towards Shane Long, whose close-range header was saved by Brad Jones at full stretch.
Boro had chances as Gary O'Neil then Barry Robson saw efforts from the edge of the box saved before they took the lead two minutes after the break
Justin Hoyte crossed from the right for Killen to send a header looping over Adam Federici.
Reading hit back with Kebe beating Emanuel Pogatetz on the left and racing along the byline before cracking in a low shot that deflected in off the unfortunate Wheater at the near post.
And Reading almost snatched the win two minutes from time as Glyfi Sigurdsson's fierce 25-yard free-kick was palmed into the air by Jones, who then tipped the ball over the bar under pressure.
Visiting boss Brian McDermott was delighted with his side's display.
"We did well, " he said. "Boro are a good team with a lot of quality and this is a tough place to come to.
"We had a bit of a setback when they scored but it was early enough for us to regroup and we showed character to do that.
"Obviously a lot of that is to do with the confidence you get from a good run but it it is also because we worked hard and kept our shape and I think got what we deserved.
"In fact if anyone was going to win there at the end it was us but I was pleased and we'll take the point."
McDermott laughed off suggestions Reading themselves could launch a late bid for the top six.
"I'm just glad to be out of the bottom three," he said.