Pompey fans chanted for Kenny Jackett to be sacked as the team succumbed to a late defeat at Kingsmeadow.
Video of a section of the away support immediately on the final whistle shows them chanting 'We want Jackett out, we want Jackett out' before and after the final whistle.
Some supporters angrily gesticulated towards the dugouts - which were right in front of where the 700 Pompey fans were accommodated - as Jackett and other backroom staff went on the pitch at the end.
The pressure has been growing on Jackett during Pompey's poor start to the season, in which they have now won only three of their opening 11 League One games to leave them languishing 17th in the table.
There has been booing at a number of games and after last week's 0-0 draw with Gillingham, there was significant discontent around the ground.