Nathan Blake looked to have saved Bassett from the wrath of a crowd of less than 7,000 when his header soon after the break cancelled out Mixu Paatelainen's goal.
But, in the second minute of stoppage time, Alan Thompson lifted in a free-kick and Scott, trying to clear, flicked the ball past the advancing Alan Kelly and over the line.
'Alan says he shouted for me to leave it but I just didn't hear him,' Scott said. 'I've got to hold my hand up and say it's my fault but the ball just flicked off my head and went in.'
Bassett said: 'We must have upset somebody up there. Alan shouted but Andy didn't hear him - that's the way things are going at the moment.'
Pat van den Hauwe played with a suspected broken right leg for almost 10 minutes in the first half of Millwall's 2-0 victory at Third Division Mansfield. The former Everton and Tottenham defender injured his right leg in a tackle with Mansfield's Simon Ireland and hobbled on for several minutes before being substituted.
Mick McCarthy, whose side eased through with goals by Richard Cadette and Mark Kennedy, said: 'It looks like the damage to Pat's leg could be quite bad. It could be a fracture. I am keeping my fingers crossed.'
Mansfield, who had their full-back, Adrian Boothroyd, sent off in injury time for abusing a linesman, almost snatched an equaliser when Paul Holland missed from point-blank range. But Kennedy put the game out of reach with a goal in the 89th minute.
'At the end of the day we are a Third Division side playing a team two divisions higher,' Andy King, the Mansfield manager, said. 'I am pleased we didn't disgrace ourselves.'Reuse content