Stanley threw away a one-goal lead to draw with Pompey on Saturday.
Sean McConville opened the scoring for the visitors just 44 seconds into the second half, before Ben Close equalised in the 59th minute.
The spoils shared meant Kenny Jackett’s side finished fourth in the League One table going into the play-offs, with Accrington ending the campaign in 14th.
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After breaking the deadlock, Coleman was disappointed his troops didn’t extend their advantage, while he felt the visitors had a couple of claims for a penalty.
But the Stanley boss did heap praise on Close, who netted his ninth goal of the season.
Coleman told BBC Radio Lancashire: ‘I’ll be honest, I’m disappointed we didn’t win the game.
‘We got into the lead, which was thoroughly deserved, and could have gone further ahead.
‘Our keeper hasn’t really made too many saves. They hit the post with a screamer and we hit the bar in the first half.
‘The goal was a bit disappointing. We lost runners in midfield and it was a good finish to be fair for the lad (Close).
‘We felt we could have stopped that and had defended well.
‘We made some great chances and on another day we might have had a couple of penalties.
‘Not many teams will come here and do what we did, which was dominate the game and create a lot of chances.’
Having survived in League One by five points after being promoted last season, Coleman is now planning for next season.
The Liverpudlian revealed he’s already earmarked several potential recruits during the summer transfer window.
Coleman added: ‘The first thing I need is a rest because it’s been mentally demanding more than anything.
‘I’ve already got my eye on players and there will be an overhaul of players.
‘But we do have the nucleus of a squad, have a good side that play the game the right way and show a lot of passion, fight and skill.’