"The feeling is not so great because of the way we conceded the last goal", Spurs boss Mauricio Pochettino said.
Publicly at least, Tottenham is not blaming Wembley where it will play all its matches this season.
Spurs followed last Sunday's defeat to Chelsea at the national stadium with another disappointing result, but Pochettino said their failure to win was a "collective mistake". "That is football. It was a tough game".
But Tottenham finally breached the visitors' defence four minutes after the restart when Ben Mee mangled his attempt to clear Dier's flick-on and Alli slotted away the stray ball at the second attempt.
Burnley sensed the unease in the Tottenham ranks and Wood, on as a substitute, latched on to a pass from Robbie Brady to fire past Spurs keeper Hugo Lloris in the 92nd minute. We have the responsibility to do better, to try to win.
They looked on course to win through not the prettiest of goals in not the prettiest of matches.
It wasn't the most attractive of goals as he got on the end of a Christian Eriksen corner kick. The only way to fix conceding is to work hard during the week.
Lamela is doing outdoor work as he works his way back from a hip problem that has plagued him for almost a year, while NKoudou is set to return from a foot injury after the forthcoming global break.