The summer signing felt the Blues side that took to the pitch for opening 45 minutes let their standards slip.
Pompey had to come from behind twice to beat the National League South Hawks after stunning strikes from Tommy Wright and James Roberts.
Tunnicliffe's first goal for the club had drawn Danny Cowley's team back level in the first half, before Roberts' curling strike gave the hosts a 2-1 half-time advantage.
Pompey's first-half side, which included the likes of Tunnicliffe, Shaun Williams, Ronan Curtis and John Marquis, were replaced by 10 new players at the break.
Triallist and former Norwich striker Gassan Ahadme struck a second-half hat-trick, while Reeco Hackett-Fairchild ensured the Blues turned things around to run out comfortable 5-2 winners in the end.
However, Tunnicliffe conceded he and his team-mates who featured in the first half could not be happy with their efforts against Paul Doswell's men.
He said: ‘It’s early days but I think it’s important to set standards early on. It’s only our second game, but I don’t think we can come here and perform the way we performed because that’s not winning habits.
‘We want to win every game we play so to come off 2-1 down at half-time was disappointing for me personally - and I know that was the case for the other boys that played.
‘Thankfully, the second-half team have dug us out of a bit of a hole.’
The two teams were roared on by a crowd of around 3,000 at Westleigh Park.
It was a welcome sight and the first time head coach Cowley had taken charge of a fixture in front of the Blues faithful.
For Tunnicliffe, it was his maiden opportunity to play in front of Pompey supporters - and a welcome at that.
He added: ‘It felt like a proper game when everyone was cheering.
‘Obviously, as players, we’ve all missed it, so it was great to see a full house here and buzzing for it.‘I’s been a tough two weeks for us, no excuse, and we look forward to a good week at St George’s Park.’