Iain Hume scored the only goal of the game when he prodded home Martin Woods' cross from the left after 24 minutes after Pompey goalkeeper Mikkel Andersen and skipper Brian Howard hesitated to clear.
"I think we deserved three points - most definitely," said Whittingham. "They did what I asked them to do and put plenty of balls into the box. We had plenty of efforts on goal and it just hasn't been our day for finishing.
"You wouldn't have thought there had been five defeats in a row before this game. I don't think that was a team playing without confidence. We did the right things and we have to do that on Tuesday night against Leyton Orient."
Whittingham was pleased with an exciting debut from loan signing Nathaniel Mendez-Laing, who was a constant menace to Rovers following his move from Peterborough.
"I'm very pleased with Nathaniel. He started to get people on their feet when he got the ball. He showed he has the ability to run at people and create things for us," said Whittingham.