The corporation previously issued an apology after broadcasting footage of Eriksen receiving urgent medical care.
The Danish midfielder made headlines the world over when he suddenly collapsed during Saturday's Euros match.
The BBC previously issued a public apology over the broadcast.
Eriksen was taken away on a stretcher and has been stabilized.
In getting Spurs to the Capital One Cup final and keeping them in contention for the Europa League and a top four Premiership finish, Pochettino is having a remarkably good first season. To the more delusional Spurs fan this level of achievement might be considered par but given what he's had to contend with, it is much better than that.
Happily there is no talk of losing Harry Kane, the lifelong Tottenham fan who hails from nearby Chingford and has risen from the ranks. Dare the faithful hope that his journey from likeable trier to deadly operator might be similar to the one the team is on?
An away win at high flying Swansea, an emphatic cup quarter final victory over Newcastle and, finally, the defeat of a lowly premier league team at home after the debacles against Stoke, West Brom and Palace have meant that Christmas has arrived slightly ahead of schedule for Tottenham fans.
Somehow, despite all the moaning, the turgid play, the ordinary players, Franco Baldini, Poch's accent and the small pitch, Spurs are just four points off the top four, two points behind Arsenal, three clear of Liverpool and still in all the cups. But without Eriksen, the picture would be a good deal less rosy.
Perhaps it's sod's law that three days after they've finally put together a good performance Spurs have to go to Chelsea who look more or less unbeatable. On the other hand, maybe this is exactly the right time to visit Stamford Bridge...
Tottenham manager Tim Sherwood labelled his Benfica counterpart Jorge Jesus "classless" after the clubs' Europa League tie