Leeds manager Peter Reid refused to resign after his team's latest setback, a 6-1 thrashing on the South Coast which was Leeds' heaviest defeat in the Premiership.
For an hour, Leeds were matching their hosts until a collapse in defence led to a humiliation and put a doubt about Reid's ability to carry on as manager at Elland Road.
Reid said: "I will not give up. I thought we did okay in the first half, but the second half was an absolute shambles in terms of desire and wanting to win.
"This was the worst 45 minutes of my career as a player and a manager without a shadow of doubt.
"It is not a lack of confidence. We gave away a couple of goals but the attitude was not right. We are in a desperate situation and some players do not realise it.
"Once we had 3-1 down, white flags went up all over the pitch." Dejan Stefanovic put Portsmouth ahead in the 16th minute with a header from a corner by Patrik Berger, but Alan Smith equalised three minutes later with a crisp left-foot shot.
Until first-half injury time Leeds, who had lost six of their previous seven matches, were on level terms and giving as good as they received.
But then a speculative volley from 30 yards by Gary O'Neil deceived Paul Robinson and Leeds collapsed. The turning point was a fine save on his line by Shaka Hislop from Jermaine Pennant in the 47th minute.
From that moment Leeds fell away and it was no surprise when Portsmouth made it 3-1 in the 63rd minute with a right-foot shot from Hayden Foxe which Robinson touched but could not keep out.
O'Neil, playing his first match of the season, finished off a pass from Berger in the 71st minute and the floodgates opened. Berger ran clear after 75 to go around Robinson for the fifth and Yakubu Ayegbeni at the second attempt made it six in the 86th.
Portsmouth manager Harry Redknapp said: "Things change rapidly in football. A couple of years ago I thought Leeds were going to dominate for a decade while Portsmouth was a club going nowhere." To add to Leeds' misery they had Smith, Seth Johnson, Dominic Matteo and Salomon Olembe all booked for fouls.