Boro trailed 1-0 at the Macron Stadium three days after losing to the only goal at Leeds, but strikes from Grant Leadbitter and Kike eventually secured a 2-1 win.
Clayton, who was making his full debut for the club, told the official website: "You couldn't ask for a better night. It was a good win and a good performance. The way we won the game was great.
"We went behind and came back which showed the dressing-room character and that we are all together. When they got the goal, we galvanised and got round each other.
"I think it shows the spirit in the dressing room, how together we are all that we can come back after a very disappointing loss to Leeds in the last minute.
"To turn that around in three days shows that the lads are all together and what we all want to achieve."