The gesture surely confirmed he will move on when his contract expires this summer.
When Beckford failed to challenge Southend goalkeeper Steve Mildenhall in the 38th minute, he was jeered by his own supporters who shouted "You're not fit to wear the shirt" and chanted the name of fellow striker Luciano Becchio.
Beckford, who has failed to score for a month, sportingly accepted being replaced by Becchio in the 58th minute and two minutes later Max Gradel opened the scoring for Leeds with a deflected 15-yard shot off Pat Baldwin after taking a pass from Robert Snodgrass.
Becchio then delighted the home crowd by heading Gradel's chip into the net in the 83rd minute.
Troubled Southend were so short-handed that manager Steve Tilson could name only five substitutes, but with captain Adam Barrett outstanding in defence, Leeds had to graft for the win.
Matt Paterson went closest for the relegation-threatened Shrimpers with a long-distance lob in the 39th minute.