The Blues led twice in 90 minutes in the capital, but twice surrendered their advantage as defensive mistakes hindered Danny Cowley’s side for the second consecutive match.
Ronan Curtis’ worldie handed Pompey the lead but the Blues, similar to that to Plymouth in midweek, couldn’t double their lead before half-time.
Cowley’s side were then made to rue missed chances during the opening 45 minutes as Charlton equalised two minutes after the restart.
The former Southampton manager, who was given merciless stick by the 3,000 travelling fans who were in fine voice, then revealed how a tactical tweak helped bring his side back level, after his side’s poor start to the game.
Adkins’ change in tactics worked once again after Marcus Harness had looked to have handed Pompey their first win in six games, but Josh Davison tapped home from close range on the cusp of full-time to extend the winless run.
Speaking to South London Press Adkins explained: ‘We responded in the right manner. We conceded, from our point of view, a too open goal. So, we went behind early doors but the players responded in a really good manner.
‘We gave a poor goal away. Elliot Lee hit the post, we could have got a goal back straight away. We changed the shape after 15 minutes, I think that was important for us to get a foothold back in the game.
‘Second half we made a substitution. Sean Clare scored more or less with his first touch. The Valley was rocking, it was a fantastic atmosphere.
‘Our players have shown great spirit again. Having a right good go for each other. We’ve conceded a second goal where we had the ball in the attacking third so we’ve been done on the counter attack.
‘So, a change of shape, substitutes coming on and impacting the game and scoring goals helped. Great spirit amongst the players. Fantastic atmosphere in The Valley.
‘We’re disappointed we haven’t got three, I’m sure the opposition are disappointed they haven’t got three. Both of us have to settle with one.’