The Seasiders, languishing in the bottom two of the Championship, held their own in the first half against their Premier League opposition in what was new boss McCarthy’s first match in charge.
But they were behind at the break after Perraud scored directly from a free-kick, and the French full-back then extended his side’s advantage midway through the second half before Charlie Patino pulled a goal back.
The result ensures Southampton are one win away from reaching their fourth FA Cup quarter-final stage in six seasons.
Saturday was Saints’ second cup clash in five days, having lost the first leg of their Carabao Cup semi-final to Newcastle 1-0 on Tuesday and led boss Nathan Jones into making eight changes.
Mislav Orsic was first to test Chris Maxwell as he curled an effort wide of the Blackpool keeper’s left post after four minutes.
Maxwell then avoided conceding an early opener when he beat Sekou Mara’s diving tackle inside the six-yard box to clear, with the Saints striker picking up a booking in the incident.
The hosts were the brighter side in what was a slow start to the period, with few chances for either opponent by the 15-minute mark.
Orsic tried to get something started when he latched onto a cross from the right and laid it off to Perraud, but it was too tight an angle for a shot.
It was not long, however, before the Frenchman netted the opener.
CJ Hamilton was booked for bringing down Samuel Edozie at the edge of the area, and Perraud wasted no time as he struck the resulting free-kick directly into the bottom left of the net.
The Seasiders came close to levelling when Jerry Yates fired a composed strike at Willy Caballero, who leapt to tip it well high of the woodwork, and enjoyed a late first-half surge but could not make anything from a corner or a free-kick.
Southampton survived an early second-half scare as they let Yates play Ian Poveda through on goal from the left. Caballero came forward to stop the initial attempt from inside the area, but was only able to block the initial attempt.
Poveda pounced on the rebound as the Saints keeper and two defenders scrambled back to the goal-line, breathing a sigh of relief when the Blackpool forward directed his effort wide.
The hosts made it 2-0 after the restart when Perraud latched onto a quick touch from Mara inside the area and fired a left-footed strike past Maxwell into the bottom-right corner.
Blackpool cut the deficit within five minutes when Poveda fed Patino, who finished with a low, close-range effort into the bottom-left corner to deny the hosts a clean sheet. A quick VAR check determined there was no offside in the build-up and the goal stood.
Substitute Theo Walcott nearly made it three for the hosts when his effort from the right took a deflection off a blue shirt and bounced dangerously close to the goal-line before landing on the roof of the net.
Saints staved off the Seasiders in six minutes of added time, Che Adams blocking Callum Connolly’s nodded effort and Caballero getting his gloves on Charlie Goode’s header to wrap up the win.