Sturrock's appointment came as Southampton were accused of using the same recruitment tactics that destroyed Hoddle's hopes of a return to the club.
Hoddle left Southampton for Spurs mid-season three years ago, but now it is the Saints who have done the poaching by luring Sturrock.
Plymouth vice-chairman Peter Jones said: "We are extremely disappointed, in fact devastated, with Southampton, who have done what Spurs did to them with Hoddle. We can't keep a man who doesn't want to be here."
Sturrock had signed a new fiveyear deal at Plymouth last summer but a clause inserted in the contract allowed him to talk to Premiership clubs.
His appointment was also criticised by Saints' supporters, who admitted that it made Lowe's attack on Tottenham's "north London yobbos" look hypocritical.
"We've done exactly the same to Plymouth as we accused Spurs of doing to us," said Nick Illingworth, of the Southampton Independent Supporters Association.
Hoddle opted to withdraw from the race yesterday, claiming he did not want to split the board by taking the helm, though the reaction of Southampton's furious fans may have contributed to his decision.
Hours later, Sturrock, who quit Dundee United in 2000 fearing he was heading for a nervous breakdown, headed along the south coast to meet Lowe.
Plymouth vice-chairman Jones said he could not blame Sturrock for wanting to step up.
"We love him. We're desperately sad to lose him," he said. "But a man of that calibre, if he gets the chance to pit his wits against (Arsene) Wenger and Sir Alex (Ferguson) and so forth, those opportunities don't come very often."
Grimsby today appointed Nicky Law as their new manager until the end of the season. Law, who left Bradford in November, replaces the sacked Paul Groves. Caretaker Graham Rodger stays at the club as Law's No2.
