The 19-year-old - a surprise summer signing from Burnley - was one of eight players brought into the first XI by Ange Postecoglou for the clash with the Championship side, making his third start of the season.
However, Odobert was only on the pitch for 18 minutes before having to be replaced with an injury, which according to Spurs journalist Alasdair Gold appears to be hamstring-related.
Gold reports that Odobert was sprinting back after losing possession before dropping to the turf, and he gingerly trudged off the field as Brennan Johnson came on in his place.
Postecoglou should deliver an update on Odobert's issue in his post-match press conference, but the teenager has already emerged for upcoming clashes with Brentford, Qarabag and Manchester United before the end of the month.
Tottenham are also without Richarlison and Yves Bissouma due to their own fitness problems, although Micky van de Ven and Dominic Solanke both recovered from their concerns before the weekend's North London derby loss to Arsenal.