Coppell's side were beaten 3-0 at home by Millwall on the opening day of the Championship season on Saturday.
And only a series of fantastic saves from Dean Gerken stopped them suffering another heavy defeat at Roots Hall against their League Two hosts, who triumphed after extra-time with striker Matt Paterson bagging the winner on Tuesday night.
He headed home a left wing cross from Ryan Hall in the 104th minute having previously cancelled out Jamie McAllister's early opener from the penalty spot in the 31st minute.
City regained the lead eight minutes from the end of normal time with Ivan Sproule sliding home a cross from Albert Adomah.
But six minutes later, Southend were back level to send the tie to extra-time as Barry Corr headed past Gerken after being teed up by Scott Spencer.