Wolves manager Dave Jones admitted he faced a dilemma after his side crashed at the Riverside Stadium.
Jones was reflecting on the controversial first goal that gave Middlesbrough a vital breakthrough.
Gaizka Mendieta scored following a quick free-kick while players were still arguing.
Jones said: "It is very difficult for me as a manager when I look at the first goal. Do I have a go at my players for switching off or do I have a go at them for trying to stop a fight.
"Mendieta struck his goal very well. I could not see Middlesbrough scoring before that. They were not putting us under any pressure and we were getting to grips with the game.
"When you look at the millions of pounds they have spent, there was nothing between the sides on the day." There was limited entertainment value before Mendieta struck his first gaol since moving from Lazio.
Goalkeeper Michael Oakes was left helpless as he blasted a powerful shot from outside the penalty area.
As Middlesbrough celebrated the visiting players surrounded referee Steve Dunn with their protests.
Brazilian star Juninho, who has been in the shadows in recent weeks, thrilled his admirers with his match-clinching goal in the final stages from a perfect Boudewijn Zenden pass.
Middlesbrough manager Steve McClaren admitted Wolves made it difficult for his side.
"In tight games like this you are looking for something special and we got it from Gaizka Mendieta.
"Mendieta and Juninho are very special players and they proved that today because they won the game.
"It has been a great week with four points from two games, a Carling Cup win, and our fifth clean sheet of the season." There was an angry melee among players in the tunnel after the game.
Jones admitted: "I was in the middle of it," without revealing what happened.
The referee is to send a report to the FA. McClaren said he did not see the incident because he went into his room after the final whistle.