Hart, Portsmouth’s director of youth operations, was put in charge of the first team until the end of the season after Tony Adams was sacked in February.
A board meeting is scheduled for next week, when a decision will be taken on the way forward in terms of the next manager, but Hart declined to say whether he wanted the job.
“I think this week will answer most questions about the managerial position and players,” he said.
“We have been concentrating on getting these games out of the way. Fortunately we became safe last week, which was important for us.”
Colombia striker Hugo Rodallega scored the game’s only goal in the 27th minute when he tapped home from three yards after Sol Campbell had allowed Charles N’Zogbia’s cross through his legs.
Steve Bruce, the Wigan manager, paid tribute to winger Antonio Valencia after he put in the kind of display which has attracted the interest of the likes of Real Madrid and Manchester United.
“He showed why we will struggle to hold on to him, he was absolutely magnificent,” Bruce said.
WIGAN (4-4-2): Kingson 6, Melchiot 7, Boyce 7, Bramble 7, Figueroa 7, Valencia 8, Cattermole 6, Brown 6, N’Zogbia 6 (McManaman 78, 5), De Ridder 7 (Routledge 90, 5, Rodallega 7.
Subs Not Used: Pollitt, Edman, Cho, Watson, Kupisz.
PORTSMOUTH (4-4-2): Begovic 6, Kaboul 5 (Kanu 72, 5), Campbell 6, Distin 6, Hreidarsson 4, Pennant 5 (Thomas 72, 5), Hughes 6, Mullins 5, Traore 4, Utaka 5, Crouch 6.
Subs Not Used: Ashdown, Primus, Pamarot, Cranie, Basinas.
REFEREE: Phil Dowd (Staffordshire) 6: His fussiness caused some disgruntlement but was generally sound.
MATCH RATING ** Wigan hardly had to break sweat.