Connolly's second-half double to take his tally to four goals in three matches helped lift battling Pompey off the bottom of the table at the Shakers' expense.
Whittingham said: "The quality he brings he had been a great addition for us. The goals he brings, the quality you need sometimes in a league one match.
"People can learn off him the desire to win, his attitude. He spoke at half-time and demanded improvement and he showed his experience with the goals."
Whittingham also revealed a half-time rollicking helped turn the relegation encounter in Portsmouth's favour.
He said: "It was the stereotypical game of two halves. Bury were the better team in the first half but we played well after that.
"We just had to remind the players what we had to do. To start with we allowed Bury to get at us instead of us getting at them"