Agyemang struck his fourth goal of the season in the 65th minute, just five minutes after coming off the bench, and it was a brilliant effort as he turned inside a defender on the edge of the box and then fired past goalkeeper Ryan Clarke with the outside of his right foot.
Whittingham said: "It was a fantastic goal and to do that so soon after coming on was tremendous.
"Pat's showed a lot of ability this season. He's the fulcrum of the side and he's played a lot of games so we wanted to give him a bit of a rest.
"But he had a great impact when he came on."
John Marquis added a second goal in the 82nd minute, heading in a fine right-wing cross by Yassin Moutaouakil.
Whittingham added: "I'm pleased for John too. He works hard and he's got an egg on his head from a challenge in the first half.
"He missed one just before he scored but he kept going and took the second chance well.
"After a good win (against Rochdale) last Saturday, it was important to keep the momentum going.
"But we weren't at it in the first half, we didn't show enough desire, I felt, and we were fortunate to come in at 0-0 at half-time. We had to improve and we did.
"We weren't putting them under any pressure in the first half and nobody takes any credit for that showing but as soon as we did close down and hassle them, we were a different side.
"They were on top of us and we were let off the hook really. But at least we defended well and then in the second half, with much more work-rate, we got our rewards."