Defeat by Southampton at St Mary’s left Wednesday in 16th place but only four points above the League One drop zone with 10 fixtures remaining.
Wednesday can have no complaints about the outcome, only debutant goalkeeper Richard O’Donnell standing between them and a far heavier defeat.
Southampton had to wait an hour before scoring their first goal through Jose Fonte but that did not fool the Wednesday manager.
Megson said: “We are in a relegation battle. I know that might be a shocking statement but it needs to be made.
“We have a game in hand and it is at home, which should be an advantage. But, on the other hand, we have not been winning our home games.’’
Megson has challenged his under-performing players to prove they can handle the pressure and keep the club in the division.
“People have to step up. You find out a lot about players at a time like this and if they can hack it or not.
“This match was pretty even for an hour but, as so often in tight matches, it can turn on one incident.
“We had one player not doing his job at a set piece and it has cost us. Southampton took momentum from that and got another and it was all over.’’
Rickie Lambert got Southampton’s second in the 66th minute but Megson refused to lay any blame at the hands of rookie O’Donnell.
“The keeper did well. He pulled off a couple of good saves and did not have a chance with either goal. He did well for himself and the team.’’
Southampton: Davis; Butterfield, Fonte, Jaidi, Harding; Oxlade-Chamberlain (Guly 77), Hammond, Chaplow, Lallana (Seaborne 90); Lambert, Barnard (Forte 86). Unused substitutes: Bialkowski, Richardson, Martin, N’Guessen.
Sheffield Wednesday: O’Donnell; M Morrison, Reynolds, Batth, Jones; Osbourne (Johnson 62), Miller (Potter 73), Coke, Teale (O’Connor 81); Heffernan, Madine. Unused substitutes: Cuff, Spurr, Buxton, Mellor.
Referee: G Deadman (Cambs).
Man of the match: Richard O’Donnell.