Batt unleashed a 25-yard half-volley 14 minutes from time as thehome side twice battled back to cancel out a pair of Dave Kitson goals.
Back of the net: Dave Kitson celebrates scoring Middlesbrough's second goal
But Cooper's joy was tempered as he saw Batt pick up a fifth booking of the season for going into the crowd to celebrate his goal. That now means a one-match ban.
Cooper said: 'Shaun deserved his chance to go on after doing well in the reserves in the week. I certainly haven't seen him do anything like that before.
'It was a stunning goal ruined only by the fact we now lose him for a game due to the craziest rule in football.
'How can you expect a young lad not to be excited about scoring an equalising goal against a club as big as Middlesbrough?'
Boro boss Gordon Strachan's wait for a first victory continued but he refused to dwell on having a late penalty claim ignored when Sean St Ledger went down under an Aaron Mclean challenge.
Strachan said: 'The penalty is not even worth having a debate about. We had more than enough chances to win the game but there was far more right with our performance than wrong.
'We could quite easily have won three of the four games that I've now been in charge for.'
Explore more:People:Dave Kitson, Gordon Strachan