An extended spell as a bit-part player has led Roberts to question whether he has a future at the club, but Allardyce hopes the Grenada international's first goals since mid-September will spur him on.
"We've been waiting for that for a while for Jason," Allardyce told Radio Rovers. "He's been out of the side because he hasn't played as well as he had been doing at the start of the season.
"But he's come back with a vengeance and two goals in 45 minutes is what we are looking for."
Roberts, who knows he is not first choice, is frustrated at his lack of first-team chances this season and admits he does not know what the future holds.
He and fellow striker Benni McCarthy - who also came on for the second half against Pompey - have both suffered from a switch in formation by Allardyce which has seen midfielder David Dunn playing just behind a lone front man.
Just over 11 months ago the strike pairing provided the partnership which got Rovers out of trouble when Allardyce took over in mid-December with the club in deep relegation trouble.
However, on-loan Chelsea forward Franco Di Santo is now first choice up front but his temporary spell could come to an end in January, which would give Roberts and McCarthy renewed optimism.
Roberts remains confident he can still do a job in the Premier League, although he does not know whether that will be long-term with Blackburn.
"It's not a case of having something to prove. I'm quite confident in what I can do and my record speaks for itself," he said.
"I guess time will tell, I'll have to see. I want to play football and you are always frustrated when you are not playing.
"I'll just keep plugging away and the manager can make the decisions he feels are right."