The visitors got nothing from the officials with a sending off to add to their woes.
Cotterill said: "It probably changed the game when we had a player sent off because I felt we were well into the game at that point.
"I don't want to make any excuses as I haven't seen the incident on video but our player has a gash on the side of his face.
"And I don't know whether Bothroyd should also have been sent off.
"We have been on the back end of some poor refereeing decisions and it wasn't even a free-kick before they scored their second goal."
With survival assured and the play-offs out of reach, Cotterill's men have little to play for in their final four outings.
The manager admitted that was a factor as his side succumbed to defeat.
He added: "We looked as though we were running on empty and as if our boys were waiting for their holidays.
"If we had a full side with plenty of energy then we may have got something out of the game.
"Normally as the season goes on the bookings tend to go down but I don't even want to speak to the referee because I will only get into trouble."
Cardiff counterpart Dave Jones took a contrasting view to Cotterill on the red card incident.
City had gone in front prior to the red card when Olofinjana nodded home and they cruised to victory thereafter.
Bothroyd doubled their lead on the verge of half-time after latching on to Craig Bellamy's header before the on-loan Manchester City star set up Whittingham to round off a fine display.
Cardiff are back up to second following the win and Jones said: "It was hard earned because the expectations at this club are huge and it was another good performance by us.
"The referee got the sending off spot on as their player definitely head-butted Jay Bothroyd.
"It made life a little easier for us as we knew it would be tough today but every one of the players were focused on their jobs.
"Every single player was on top form and Craig Bellamy deserved a goal as he set a very high example.
"But every one of our players worked hard throughout the 90 minutes."