In a close contest between League One rivals, played in torrential rain and hail, Scott Golbourne's goal took the tie back to Molineux after Oldham went in front through Genseric Kusunga.
Jackett said: "It was a typical cup tie and Oldham's crowd rose to it, but we have come away unbeaten.
"We didn't necessarily do enough to put the game away when we had spells of domination and the superior chances.
"It was a dominant first-half performance and we should have been in front.
"The second half was more 50/50 but, considering the conditions, I'm not disappointed with the result or with the heart that we showed.
"The weather made it difficult to play at times but we showed terrific spirit. There are things we need to do better but for spells we looked like the side I want us to be.
"It became a battle and after going behind we got back into the game with a battling performance.
"We put on an extra forward because there are times when you go for it instead of holding on to what you've got.
"It could have gone either way but we look forward to the replay."