League Two club Leyton Orient have made an unbeaten start to the 2020-21 campaign
Several of the squad tested positive after Saturday's draw with Mansfield.
This season, English Football League clubs do not have to do mandatory coronavirus tests on players and staff.
"If I was doing this again I would not do the testing," Orient chairman Mark Travis told BBC Radio 5 Live.
"This is an incentive not to test and that is bad for football and bad for health and safety."
League Two side Orient have been doing medical questionnaires every morning and said they would pay for testing to be done before Tuesday's cup tie, but Premier League opponents Spurs offered to cover the cost.
"That's why we can't be punished over this," Travis added. "People should be incentivised to take the test, especially when Premier League clubs with their resources give us the opportunity to have all our players tested."
Discussions are ongoing over the implications of not holding the third-round match on Tuesday, with a further update to be provided in due course.
Tottenham are in action in the Europa League on Thursday.
The decision to call off the match was announced two hours before the scheduled 18:00 BST kick-off at the Breyer Group Stadium.
Orient shut down their east London home and training ground after receiving the positive results following their league match against the Stags at the weekend, and held discussions with Public Health England about whether any further action needed to be taken.
This season, English Football League (EFL) clubs do not have to carry out mandatory coronavirus testing of their players and staff.
"Leyton Orient, the EFL and the relevant authorities are conducting a thorough review of the club's Covid-19 secure procedures with the view to reopening the stadium and training ground as soon as possible," a statement said.
There is little room to rearrange the tie, with the fourth round of the EFL Cup scheduled to take place next week.
Last week's draw handed Orient or Spurs a home tie against Chelsea or Barnsley.
Tottenham face Shkendija in the third qualifying round of the Europa League in North Macedonia on Thursday and, if they progress, the north London club will have a play-off match to qualify for the group stage seven days later.
Tuesday's match was set to be the first competitive meeting between Orient and Tottenham since January 2001.
Spurs had previously announced they would donate their match shirts to the foundation set up in memory of their former player Justin Edinburgh.
Edinburgh was manager at Orient when he died at the age of 49 after suffering a cardiac arrest in June 2019.
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