Wesley Hoedt took advantage of some slack West Brom marking to head home his first goal for Southampton just 11 minutes in.
The club's chairman, John Williams, and chief executive, Martin Goodman, were sacked this week because of the team's poor performances.
Dusan Tadic doubled the visitors' advantage on the counter-attack after the break, and Southampton held out despite Salomon Rondon's spectacular volley pulled a goal back.
Some frustrated Albion fans booed when Barry sloppily gave away possession at the start of the second half, while a few more jeers were audible when the former England global was replaced after 72 minutes.
Four senior players from WestBromwichAlbion have been questioned after a taxi driver in Barcelona accused them of stealing his vehicle.
"Yeah, absolutely. I think the second half proved that", said Pardew, who has won only three of his 17 games in charge in all competitions since taking over in November.
Sheffield Wednesday held Premier League side Swansea as visiting manager Carlos Carvalhal made his first return to Hillsborough since being released by the second-tier team on December 24.
The FA Cup fifth round tie between Sheffield Wednesday and Swansea City ended goalless. Laurence Griffiths Getty Images
The club itself also issued a statement on the incident, insisting they have "instigated" their own internal investigation as "the players will be subject to the full rigours of our internal disciplinary procedures".
Pardew said: "They are good people and I was disappointed if I am honest but the club made that call".
Two of those involved in the incident, Jonny Evans and Gareth Barry, both started against Southampton on Saturday after apologising for their part in the incident although Evans was stripped of the captaincy.
'I cancelled everything over Christmas, we didn't do anything socially.
"Every single game we must improve and draw some conclusions on the positives and work on the negatives because every single game from now is more and more important". But we still got our training in.
"We've gone there to try to get ourselves ready and up for the run-in and this is obviously not ideal".
Pardew will demand a response from his players after his attempts at boosting morale in Barcelona back-fired, but he insists he is not regretting his decision to replace Tony Pulis as manager in November.
"It wasn't what we wanted", West Brom manager Alan Pardew said.