Boro started the day in fourth place but a ninth loss of the campaign saw Taunton and Weston-super-Mare leapfrog them.
Gosport are one of seven clubs separated by just five points, though Hayes & Yeading - who visit Privett Park on Wednesday - and Yate Town have four games in hand on Shaun Gale’s side.
Jamie Whisken and one-time Pompey triallist Will Spetch netted from set-pieces in the first half in Dorset as Boro trailed 2-0 at the interval.
Though they got back into the game via an own goal, they could not find late inspiration as they had done in netting twice in injury time to beat Poole on the opening day of the season.
Whisken was allowed a free header from a corner to open the scoring before Portsmouth-born Spetch converted a penalty - ‘very dubious’ according to Gale - to double the lead.
A Harry Kavanagh corner was punched into his own net by Poole keeper Mark Childs in the second period for Gosport’s consolation.
‘It was disappointing,’ Gale summed up. ‘In this league you have to be on it every week. I wouldn’t say we weren’t on it, but we didn’t start well.
‘It should never have been a corner, we made a few mistakes leading up to it, and then gave their guy a free header, which is most unlike us.
‘The penalty was very dubious. It’s frustrating, but that’s football - it happens.
‘Credit to Poole, they then made it difficult for us.
‘I’ll never criticise my players for effort - the effort was immense - but we need to do the nitty-gritty things like marking from set-pieces.’
Boro’s pre-match preparations were hit when Josh Huggins, who was due to start in central defence alongside Matt Briggs, received a late call which resulted in him leaving the ground.
‘The situation has been resolved but Josh had to go,’ revealed Gale. ‘Things never run as smoothly as you want them to - Josh and Briggsy had been immense in our previous two games where we’d kept two clean sheets.’
In a late change, Ryan Woodford - available again after suspension - came in to partner Briggs.
Elsewhere, Dulwich loanee Anthony Harris-Sealy started as midfielder Elliott Wheeler is out for at least six weeks with the ankle injury suffered in the previous week’s home win over Walton Casuals.
‘You have to be sensible about it,’ said Gale. ‘It’s only one game.
‘I’m not going to get too high when we win or too low when we lose.
‘It’s frustrating, though, that we never seemed to get carved open - the only goals we concede are soft ones.’
Next up on Wednesday are third-placed Hayes & Yeading, who ended a run of five defeats in seven league games by thumping Swindon Supermarine 4-0 away at the weekend.