Bradbury took charge of the Hawks in October 2012.
He enjoyed back-to-back promotions and guided the club to the National League for the first time in their history last term.
However, the ex-Bournemouth manager was unable to keep them in the fifth tier of English football, winning only nine of their 45 league games to date.
Jackett admitted he was sorry to hear the 43-year-old had left Westleigh Park.
But the Blues boss feels Bradbury has enough experience to swiftly find a new job.
Jackett said: ‘I’ve watched Havant once or twice this season and we played them in pre-season.
‘Paul Robinson is a coach with us and is one of their players. We talk and chat about their situation and I’m sorry to see any manager lose their job.
‘For Lee, he has got a good record and is an excellent football man.
‘His career will go on. Perhaps he will be disappointed but he was the one who got them into the National League.
‘He was a successful promotion-winning manager at Havant.
‘Speaking to Robbo, they lost some key players, including Paul Robinson himself. Brian Stock retired and basically lost the spine of their team through injury.
‘Lee is someone I know quite well. He’s been a manager quite a long time as well and is an experienced manager.
‘He won’t need my advice and he is very experienced. For Lee being a former player, he will always be welcome.’
The Hawks are already plotting their return to the National League, with ex-Sutton United and Eastleigh manager Paul Doswell linked with the vacant manager’s role, along with Worthing boss Adam Hinshelwood.
And Jackett sees no reasons why Pompey’s near-neighbours shouldn’t have designs on being promoted next term.
He added: ‘The fact that they weren’t full-time and were part-time has meant the division has been slightly too much for them.
‘Now they have the ability as a club to go up out of National League South.
‘They have shown it before and I’m sure they’ll be focusing on that.’