Spurs, already without Heung-Min Son, lost Steven Bergwijn in the first half after the Dutchman, who had only just returned from injury, hurt the same ankle, while Moura was also forced off with an ankle problem after the break.
The Dutch international was on the receiving end of a late challenge before hobbling off with an ankle problem, replaced by midfielder Pierre-Emile Hojbjerg.
The 23-year-old has struggled with fitness problems during his time in north London, missing a total of 118 days through injury since joining in January 2020, according to Transfermarkt.
Brazilian frontman Moura then limped off before the hour mark after receiving another hefty challenge from Tait.
It remains to be seen whether either will be able to face Chelsea on Sunday Premier League meeting at the Tottenham Hotspur Stadium, before travelling to face Arsenal at the Emirates Stadium on September 26.