"We felt that Bothroyd was offside when he scored, but we were unable to take our chances," he said.
"We have played a lot worse than that this season and won games, but it is still very disappointing.
"The referee claimed that Leroy Lita had handled just before we had a goal disallowed, but we also thought Bothroyd was offside when he scored.
"Hopefully the play-off race will go to the wire which will help us to get right in there, but we just weren't good enough."
The Boro defence stood still when Gabor Gyepes prodded a loose ball towards goal and Bothroyd was unmarked at the far post to steer the ball over the line.
Cash-strapped City, who return to the High Court next week to face a winding-up order over money owed to HM Revenue and Customs, should have had a penalty on the stroke of half-time when Chris Burke was brought down by Gary O'Neil. Referee Darren Deadman thought otherwise and booked Burke for diving.
The visitors should have levelled four minutes after the break when a near-post header by Lita went over the bar.
Middlesbrough did have the ball in the net on the hour through David Wheater, but the goal was disallowed and both Lita and Boro skipper Barry Robson were booked for protesting too much.
Robson forced a brilliant one-handed save from David Marshall as the Bluebirds hung on to their lead and the goalkeeper was again in action in the closing minutes to tip over a close-range header from substitute Chris Killen before palming over a Gary O'Neil free-kick.
"If we had lost it would have meant we were out of the top six so that makes victory even better," said Cardiff manager Dave Jones.
"They only had two players from the side we beat up there which shows the massive changes they have been able to make.
"The crowd were behind the players today and both deserve the plaudits for a tremendous victory.
"There is a lot of unity in this club and it was shown out there on the pitch because if you do the hard word, you get the reward.
"We were so stretched today that I had four injured players on the bench. None of them were fit enough to go on."