Adkins' team were within seconds of claiming a crucial victory in the promotion race after Billy Sharp's 89th-minute strike.
But David Norris bagged a stoppage-time equaliser for Portsmouth to leave leaders Southampton ahead of Reading only on goal difference and four points clear of third placed West Ham.
It was a frustrating finale to a dramatic south-coast derby, but Adkins doesn't expect it to have any negative impact on Saints' bid to reach the Premier League.
Asked if he thought his side would be in the Premier League next season, Adkins said: "Yes. We are taking one game at a time now. We've led the division for a long period and we go back to the top of the league.
"We did it all last season, we'll do it all this season. We'll analyse it, put it to bed and the lads are already taking care of business because we know it is a quick turnaround for Monday's game (at Crystal Palace).
"We get ourselves ready for then because that is now the most important game."
Southampton had opened the scoring through Sharp's 27th minute strike, but Chris Maguire's rasping effort levelled for Portsmouth nine minutes later.
Former Doncaster striker Sharp put Southampton back in front when his close-range effort, originally ruled out for offside, was given as a goal.
However, midfielder Norris struck deep into stoppage-time to stun the majority of the 31,743 crowd and keep alive second-bottom Portsmouth's hopes of avoiding relegation.
Fourth-placed Birmingham cemented their position in the play-offs with a 3-1 home win over Crystal Palace, but boss Chris Hughton isn't happy about having to play promotion rivals West Ham on Monday.
Hughton's side will have 24 hours less recovery time for the crucial trip to Upton Park as the Hammers played at Barnsley on Friday.
"The players will be in a very good mood. But the only disappointment from our point of view is that a side as good as West Ham at this stage of the season have an extra day rest and recovery than we have," Hughton said.
Chris Burke opened the scoring for Birmingham after 21 minutes and Keith Fahey extended their advantage 60 seconds later.
David Murphy then got his name on the scoresheet just after the half-hour before Owen Garvan got one back for Palace on the stroke of half-time.
Cardiff swept into the play-off positions with a 2-0 win at Middlesbrough that saw the Bluebirds leapfrog their opponents into sixth spot.
Bluebirds boss Malky Mackay said: "We are back in the play-offs and we have a bit of momentum behind us now.
"We have beaten a good Boro side who are one of our promotion rivals and things like that give you a little bit of a psychological edge going into the play-offs."
Leicester still have an outside chance of finishing in the top six after thrashing bottom of the table Doncaster 4-0.
Coventry dropped into the relegation zone as Peterborough drew 2-2 at the Ricoh Arena, while Bristol City climbed out of the bottom three with a 1-0 win at Nottingham Forest.
Millwall boosted their survival chances with a 2-0 win over Hull and Derby and Ipswich shared a goalless draw.