The Pilgrims threw away a two-goal lead to draw 2-2 at Fratton Park on Saturday.
Luke Jephcott thought he’d earned Argyle all three points with a second-half double.
But the Blues rallied gamely in the closing stages, with Ronan Curtis and James Bolton bagging twice in two minutes to ensure honours were even.
It meant Pompey dropped to fifth in the League One table while Plymouth moved up to 12th.
Lowe, who signed a new three-year deal at Home Park on Friday, admitted the Blues’ current position is what his club is inspiring towards.
And he had mixed emotions about the stalemate at PO4.
Lowe told the Plymouth Herald: ‘They are the heights we want to get to. They are fourth or fifth in the league and they are going for promotion – and rightly so.
‘They are way above our budgets and everything else – and blows everyone out the water – not that I’m complaining.
‘I feel we have got a good squad and we do things the right way. We dealt with a lot of long balls.
‘So, to sum it up, I’m disappointed because we have lost two points but I’m also pleased and proud of the boys the way they committed themselves for 85 minutes of the game.
‘There are a lot of people that probably wouldn’t have given us a chance coming to Fratton Park and playing the way we did.
‘We soaked up a lot of pressure, we won every header. They had five or six corners on the bounce early on, we dealt with every single one.
‘I felt we didn’t get a lot of help in the first half in terms of things not going our way. Second half was a lot better.
‘To be 2-0 up you are thinking "Okay, yeah three points" but Portsmouth are a good well-drilled team and we always knew they were going to have a moment.
‘Their moment came from our mistake. If that mistake doesn’t happen then we probably see the game out.
‘So, of course, I’m disappointed because we should have won. It’s two points dropped.
‘But I’m also pleased the way the lads were and how they reacted to coming to Fratton Park and putting on a show the way they did, being 2-0 up.’
Pompey return to action when they welcome Swindon to Fratton Park on Tuesday.