The Cherries were controversially awarded a chance to claim three points from the spot, following an apparent foul by Ryan Bertrand on Ryan Fraser.
Both sides hit the post while the game's golden chance fell Bournemouth's way with Harry Arter skying a late penalty over the bar, and by some distance.
Andrew Surman's poked effort was cleared off the line by England worldwide James Ward-Prowse, while Jay Rodriguez's thumping drive forced Cherries goalkeeper Artur Boruc into a reflex save.
"I didn't intentionally miss of course".
The south coast derby ended 0-0 at St Mary's after Arter slipped during his run-up and struck embarrassingly over the crossbar, as David Beckham did for England against Portugal at Euro 2004.
"Jack will be the one who decides his future, in conjunction with Arsenal", Howe said. Indeed, the Saints have scored a couple of times in only two of their home games all season and so we're siding with Bournemouth on the Double Chance.
Bournemouth have never won at Southampton, losing eight and drawing four of 12 league and cup games. Bournemouth do tend to struggle on their travels and if Southampton play to their best, a home victory is likely to be on the cards.
Canada supports 'limited and focused' U.S. military action against Syria, Trudeau says
The missiles struck their targets, which also included Syrian aircraft and fuel stations, at 4.40am local time on Friday. US Secretary of State Rex Tillerson said Washington had "no doubt" it was the Syrian leadership behind the attack.
"I feel if I scored we would have got three points". He also twice threatened to score before being taken off in the 80th minute.
Bournemouth manager Eddie Howe: "It should have been three wins in a row".
"We were not great in the first half but in the second we dominated the game and had great chances to put the game to bed".
Bournemouth travel to local rivals Southampton for the 5.30pm kick-off on Saturday evening.
Bournemouth fans remain optimistic of surviving relegation as the 2016-17 Premier League football season draws to a close.
The Southampton midfielder responded to his manager Claude Puel's instructions to do his talking on the pitch - after he had complained about regularly being substituted - by creating numerous chances for his team-mates.