Michael Smith's 31st-minute finish cancelled out Steve Morison's opener for David Hockaday's side, but Rodolph Austin's second-half penalty restored United's lead and that is the way it stayed.
Speaking to the club's official website after the game, Cooper said: "I thought we did okay but we need to work on being more potent and making the most of possession.
"Let's not forget, we're playing against a good Championship team.
"We dominated a lot of the ball and you could see the effect Hockaday's had on them (Leeds).
"It was a tight game and it could have gone either way."
Swindon begin their League One campaign at home to Scunthorpe on Saturday, August 9.
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