This time there was only a one goal deficit for them to recover but they did so with two Robert Snodgrass goals in the last fifteen minutes.
Grayson, who was busy fending off comments on Andy O'Brien who, he said, will never play for Leeds United again, admitted: "We were lucky to still be in the game at half time and our keeper made one or two good saves.
"Burnley dominated us in the first half but we said at half time that we needed to up the tempo. Once we got the equaliser, I felt we could go on and win the game because we had the presence of the Leeds fans trying to suck the ball into the net."
It was a frustrating afternoon for Eddie How who, apart from seeing the points lost at the end of the game, also lost Charlie Austin for a while after the leading goalscorer suffered another dislocated shoulder.
"It is a really tough one to take because I thought for the entire 90 minutes today we were excellent," Howe said after the game. "We started at a really good tempo, scored a good goal and carried that on through the rest of the first half and were well on top.
"I think Lee Grant had one shot to save in the whole game and he ended up picking the ball out of the net twice. Against a lively front two, I thought we looked really good defensively, a lot better than we have of late, but we have conceded two poor goals again, so there's huge disappointment."
He was pleased with debutant Sam Vokes and added: "We lost Ross (Wallace) during the week to a tight hamstring, so we wanted an extra attacking body and Sam did really well when he came on.
"He is a physical presence and a real handful and there are signs that he could form a really good partnership with Jay, whose overall game was excellent today.
"There are a lot of positive to take from individual performances and we looked a real threat going forward against a good side. That pleases me, but everyone will look at the result and we've lost, so the lads need to show strength of character now because this is a difficult run we are on.
"I still believe in the team and I do believe we are good enough, but the results aren't reflecting that, so we need to try and get a result as quickly as we can."