Spurs were on course for all three points in their European opener when Christian Eriksen broke the deadlock eight minutes into the second half, but their failure to add to that lead proved costly.
Mauro Icardi levelled things up late on before Matias Vecino completed a dramatic turnaround in stoppage time to condemn Spurs to a third straight defeat in all competitions - their worst run under Pochettino.
"The performance was good from the team, the result should have been different and I think everyone will agree," the Argentine told reporters after the match.
"The performance was better than Inter Milan but when we conceded after 86 minutes the game was completely different.
"The team deserved much more and I think that was our best performance since we started the season. But we lost the game."
Spurs will attempt to stop the rot away to Brighton & Hove Albion on Saturday.