The Blues conceded twice in the final six minutes of the League One clash and left the Memorial Stadium empty-handed.
Oli Hawkins’ third goal in two matches had given Kenny Jackett’s outfit the lead, with his smart header midway through the second half giving Gas keeper Adam Smith no chance.
However, Pompey were unable to shut up shop after defending gallantly for most of the game.
Stuart Sinclair equalised for the home side six minutes from time, before substitute Liam Sercombe drilled home a 90th-minute winner to snatch victory for the hosts.
And Clarke could not hide his annoyance after the Blues had all three points within their grasp.
The centre-back said: ‘It is so frustrating.
‘To battle away all game and do very well against what I think are a good side and throw it away at the end is so frustrating.
‘I don’t think you can pinpoint one particular thing. Maybe it was a bit of naivety from us.
‘We battled well all game, I just think we didn’t look like we were going to concede two goals.
‘But then to concede two is just so frustrating.
‘I’m not going to beat around the bush.
‘They were on top and had the territorial advantage and were in our half a lot more than we were in theirs.
‘But the team at the moment feel we can withstand that and we did.
‘Even the second goal wasn’t really a chance, it was a shot from a long way away.
‘I wouldn’t go as far as saying it’s heartbreaking but it’s along those lines.’
– WILL ROONEY