The duo saw red within minutes of each other as the Chelsea player clashed with Barry, before the latter was dispatched for a second bookable offence.
Asked about Costa’s red specifically, he said: “My interpretation is I don’t think it was a key moment. It was an emotional game and rightly so.
“Diego Costa had a fighting spirit and I would like to praise the referee [Michael Oliver]. The sending-off of Costa was right.
“The sending-off of Gareth Barry was right and the referee never allowed those emotions to stop the fluency.
“Whatever happens with Diego Costa I am sure the two players shook it off.
“From where it was he moved his head towards Gareth Barry and I lost sight of that action.
“I thought it was a second yellow. It was a moment that didn’t have an impact on the scoreline.”
Martinez rejected the suggestion his players had targeted the temperamental Costa.
“It is part of trying to do an interpretation as you want,” he added.
“We matched each other well. None of my players fell into the focus of losing the game.”