Pompey have dropped just two points from their opening six league fixtures of the 2018/19 campaign.
It leaves Kenny Jackett’s side sitting second in the standings and only being kept off top spot by Peterborough’s superior goal difference.
That ensures belief will be high ahead of Shrewsbury’s League One visit to the south coast this weekend.
But Jackett is not getting complacent and wants to see continual signs of improvement from his squad.
The Blues boss said: “We always hope to see a Pompey victory and our supporters are optimistic about us doing well.
“It’s not a pressure – I think it’s great. We’ve had a good start to the season and there’s belief around the place. But similarly we all know to look forward and not back.
"We’ve seen good signs of improvement and if we want to be contenders then we have to get better in all areas."
“There have been games when we’ve battled well to get points, although we knew that wouldn’t always be enough.
“We’ve seen good signs of improvement and if we want to be contenders then we have to get better in all areas.
“The bar has to remain high – this is Portsmouth Football Club and our standards should be right up there.”
Pompey’s next opponents have yet to win a game after narrowly missing out on promotion last term.
Jackett said: “Shrewsbury haven’t quite clicked yet after a fantastic season last time out. They’ve made a high amount of changes, but I do see a talented squad.
“I believe they’ll turn things around at some stage, so it’s up to us to maintain our own demanding standards.
“We’ll need everybody performing on Saturday and to make sure performance levels are as high as they possibly can be.”
Oli Hawkins, Anton Walkes and Jack Whatmough all suffered injuries against Plymouth last week, although one of them could return against the Shrews.
Jackett said: “Hawkins looks okay. He’s come back quite well and my expectation is he has a good chance for Saturday.
“I think for Walkes and Whatmough, Peterborough next week is unlikely and we’re probably looking at the week after.
“It was unusual after two months of minimal injuries to lose three in the first 45 minutes of one game.
“But you know that they’re going to come at times during the season and our substitutes played a big part last week.”
Pompey will also be without top scorer Ronan Curtis, who is on under-21 international duty with Republic of Ireland.
Jackett said: “I’ll phone Ronan and wish him all the best because it’s a big honour to represent your country.
“They have two big games in their qualifying campaign and I hope they do well, while also hoping he comes back to us fully fit.”