The 76-year-old has questioned the credentials of the south coast club's new Argentine manager, after he took over following Nigel Adkins' dismissal on Wednesday
Adkins was relieved of his duties on Wednesday - just two days after having earned a point away to European champions Chelsea - with Pochettino's arrival announced hours later.
And McMenemy, who led Saints to a 1-0 win over Manchester United in the 1976 FA Cup final and their highest-ever league finish in 1984, believes the club are taking a huge risk.
"It's not as if they have brought [Jose] Mourinho or [Pep] Guardiola in," he told BBC Sport.
"They have brought in a chap, with due respect he might be a nice man and a very good coach, but who nobody has heard of. It's a terrific risk."
Saints had lost just twice in their last 12 league games before Adkins' removal, a fact which McMenemy believes proves the club were wrong to dismiss a manager who had overseen two successive promotions.
"Normally, when a manager gets sacked it is because things have gone wrong," he continued, "but not on this occasion."
McMenemy also claimed that Pochettino needs to "hit the ground running" if he is to have any hope of steering clear of the relegation zone.
"He has got 16 games left in which he has got to get the results to keep the team up and learn English," he said. "There's a lot to be done in a short time.
"We don't know anything about the man coming in. We don't know what reaction the players will have.
"The players will give everything. There is no doubt about that. They are professionals and that is their job. But you don't win games by 11 people giving 100% all the time.
"The players will be looking to see whether the system will be the same and who he is going to pick.
"Timing is everything in sport and, at the minute, it doesn't look like the time of this decision was right. But time will tell."