Rose was again omitted from the Pompey squad as his side crashed out of theÂ CarabaoÂ Cup against AFC Wimbledon on Tuesday night.
That follows on from the fit-again midfielder being left out of the 18 for the opening-day victory overÂ Luton.
Rose was given a 24-minute outing off the bench against Blackpool on Saturday before returning to the stands in the 2-1 Dons loss.
The 30-year-old was given a new one-year deal in March and has battled back to fitness after suffering a broken leg last December.
JackettÂ explained the thinking behind his team selection with Adam May also left on the bench and not seeing a minute's action so far this term.
He opted to keep Tom Naylor, Ben Close and Gareth Evans as his midfield trio after they all started at Bloomfield Road at the weekend.
That's after optingÂ for Naylor and Anton Walkes as a central-midfield duo on the opening day of the campaign.
Jackett said: '˜I went forÂ NaylorÂ and Close and then Gareth Evans played off the centre forward. That was the selection against Wimbledon.
'˜In terms of Danny, yes, he would be thinking after his broken leg that he does need minutes but he didn't get themÂ on TuesdayÂ night.
'˜For Adam May as well he has to have opportunities and progression.
'˜Of course, Adam and Danny have both had a limited amount of game-time.'