It was the first time Tottenham manager Pochettino had been knocked out of a domestic cup competition against lower-league opposition.
The shock defeat extended Tottenham’s poor run, which included a 2-1 loss at Leicester in the Premier League on Saturday.
“Colchester made a fantastic game, it was difficult. We are so disappointed we could not score in 90 minutes,” Pochettino said.
“That’s the beauty of the competition, always something can happen. We wanted to go further but we are out.”
After finishing as Champions League runners-up last season, Tottenham were expected to kick on this season but instead they have struggled to find any consistency.
Pochettino has grumbled about the distractions of the transfer window, with Eriksen and several other players linked with moves that never materialised.
As a result, Tottenham have looked a disjointed team, with two-goal leads squandered in draws at Arsenal and Olympiakos.
The upset was the biggest setback so far for Pochettino, who made 10 changes to his side but could still call on enough quality players to expect a win against a team 71 places below them in the football pyramid.
There were debuts for 17-year-old Troy Parrott and 20-year-old Japhet Tanganga, while Eric Dier made his first appearance of the season alongside Dele Alli in midfield.
But Tottenham laboured badly and could not find the breakthrough as Colchester followed up their second-round win against Crystal Palace with an even bigger scalp on a memorable night that ranked alongside the club’s famous FA Cup success against Leeds in 1971.
With Pochettino yet to win his first trophy as Tottenham boss and the club without silverware since the 2008 League Cup, this was another blow to their flagging morale.
Holders Manchester City won 3-0 at Championship club Preston as they made a smooth start to their bid to win the League Cup for a third successive season.
Raheem Sterling’s fine solo effort put City ahead and Gabriel Jesus doubled the lead with a crisp strike before Ryan Ledson’s own goal made it three.
Gabriel Martinelli scored his first goals in English football and Rob Holding enjoyed a dream return from injury as Arsenal crushed second-tier Nottingham Forest 5-0.
Martinelli, making his first Gunners start following a summer move from Brazilian club Ituano, claimed the first-half opener before completing the scoring in stoppage time.
Defender Holding, out for more than nine months with a serious knee problem, powerfully headed home the first of four goals in the final 19 minutes, with Joe Willock and Reiss Nelson also on target.
Southampton routed third-tier Portsmouth 4-0 in the first meeting between the fierce south-coast since 2012, with Danny Ings scoring twice for his boyhood club in their first win at Fratton Park for 35 years.
Danny Welbeck scored his first goal for 11 months in Watford’s 2-1 win over Swansea.
Leicester thrashed Luton 4-0 and Everton won 2-0 at Sheffield Wednesday.