National League South Hawks were on the end of a 5-2 defeat against Danny Cowley's League One side on Saturdau.
However, boss Doswell stressed the result was meaningless and he could take a number of positives from his side's efforts - particularly in the first half.
The Blues fielded a strong line up, which included the likes of Ronan Curtis, John Marquis, Marcus Harness and Ryan Tunnicliffe, but it was three divisions lower Hawks who went in leading 2-1 at the break.
Stunning strikes from Tommy Wright and James Roberts twice handed the hosts the lead prior to Pompey turning things around with a large number of trillists featuring for Cowley's team in the second half.
But Doswell says he can take a great deal of heart from the way his new-look squad stood up to the challenge against a strong Blues side in the first period.
'After an opening 15 minutes when we were chasing shadows a little bit and trying to get organised, I thought we were excellent between 15 and 45 minutes,' he said.
'We scored two wonderful goals and also got several crosses into the box.
‘We looked a good side in that first half after the initial chasing, really.
‘I said to Bairdy (assistant manager, Ian Baird) and at half-time that’s the half that we analyse (first half) on Sunday and Monday ready for the players.
‘I knew that it was going to be a tough task and the trialists would probably give us the run around because we’ve run them really hard this week.
‘I thought to get 45 minutes out of the team to that level was really encouraging for me.
‘It’s a bit unfair on my boys, especially in that last half-hour, they were pretty much out on their feet.
‘No-one’s disappointed about the result, if you know your football - which we do - you’re looking at that first 45 minutes of football and we’re looking alright.'
It was the first time the annual friendly meeting between the teams had been staged at Westleigh Park since 2019.
The pandemic and ongoing work to install the Hawks' 3G playing surface forced the fixture to be scrapped last summer.
Doswell added: 'There were 3,000 in the ground, it looked a big crowd, they all enjoyed it.
‘All the England songs were ringing around the ground as well.
‘We’ve got to thank Portsmouth Football Club for always respecting us with bringing a first team.
‘Danny Cowley was unbelievable, they promoted the game for us on the club’s Twitter.
‘For us, I think the relationship is going to get stronger and stronger.
‘I’s been an absolutely brilliant day. The hospitality side was fully booked, they’ve had a brilliant day, I’ve spoken to everyone in there.'
Hawks’ return to pre-season action on Tuesday at Southern League Premier South club Salisbury before welcoming an AFC Bournemouth XI to Westleigh Park next Saturday.
Hawks then travel to Bristol Rovers on Tuesday, July 27, before another home friendly with Shaun Gale’s Gosport Borough on Saturday, July 31.