England held an open training session in nearby Zelenogorsk watched by hundreds of excited young fans.
Southgate confirmed Dier would retain the captain's armband, after skippering his country for the first time against Germany.
West Ham's Carroll, Reid and Ayew were shown yellow cards, while Eric Dier and Fernando Llorente were booked for Spurs.
Marcus Rashford atoned for a costly error to bring England a 2-1 home win over Slovakia in World Cup qualifier.
Spurs manager Pochettino was left bitterly disappointed by both the performance and the implications of the defeat.