Rovers had dominated the game but trailed to Lee Stevenson's 22nd minute header.
However, they plugged away and substitute Alefe Santos grabbed his first goal for the Pirates as his low shot went in off the outstretched leg of Keiran Murtagh just when home goalkeeper Alan Marriott looked to have it covered.
"I think that was two points dropped and I thought that was a lethargic display from us," Cox said. "You want to be on the front foot at home.
"We probably scored at the right time but then took our foot off the pedal.
"It was only when they scored that we started to play again and showed the power, pace and passion I wanted. It was too little, too late.
"To give my players some credit, they were immense on Tuesday against Chesterfield.
"But, like the League game, I think it took a lot out of them and there was a bit of stiffness and tiredness out there.
"Hindsight is a wonderful thing and I did have players in my squad who could have come in with fresh legs. But I am a loyal person and I thought their performance on Tuesday warranted them staying in the side.
"I have told them to go home, enjoy their weekend and come back in on Monday ready to get back on track.
"We need to stop trying to impress people and get back to what we are good at which wins football matches. I have told them not to be so conformist in trying to please everyone.
"That wasn't good enough. That wasn't us. Take nothing away from Bristol Rovers, they are not bad, worked extremely hard and came away with a deserved point. It would probably have been unfair on Rovers if we had gone on and won the game.
"We were off the pace and our mindset was all wrong. The game was too open."