Pompey striker David Connolly tapped in Yassin Moutaouakil's cross after 53 minutes to extend his side's unbeaten run to four games.
Victories in their remaining matches against Stevenage, Brentford, Sheffield United and Shrewsbury could take the club out of the bottom four.
The cash-strapped south-coast club are still facing a 10-point deduction when they exit administration, which dooms them to life in League Two for next season.
But Whittingham, keen for his side to end on a high, said: "There are four games to go and hopefully four wins. That's what we've got to do - go out and win every game.
"This one didn't go badly. There are a couple of teams with games in hand over us, but we've got the points and hopefully we can keep putting a bit of pressure on."
Whittingham's men have now won three games in a row at Fratton Park and the manager hopes his side can continue to make their home a fortress.
He added: "We've got two games left here and we've got to make sure we carry this on. The key is making sure we don't concede many goals - that gives you the platform to go on.
"The spirit has been built and the players here at this moment in time know what our fans want. They're giving their all week in, and week out and the fans, as always, appreciate it."