Spurs took the lead at Wembley in the 49th minute when Dele Alli scored his second goal of the season, and they had chances to extend their lead and shut the door on Burnley.
However, the Clarets scored an equaliser in stoppage time as Chris Wood found the back of the net to salvage a point for the visitors.
“We need to work hard to try to be stronger, because that is a mental problem that we need to fix,” Pochettino said, as quoted by the Daily Mail.
“That is why in football you have to try to work hard to fix the problems and it is clear we need to improve and increase our mental levels and become more strong.
“At the end, when you are capable to score, 1-0, and you have the chances to kill the game, you must kill it.
“OK, if you do not kill the game, you cannot show that lack of concentration at the end.”