The Fir Park striker was last week linked with a possible move to Rangers and has also previously attracted interest from a number of English clubs including Blackpool.
He added another goal to his tally during Well's 1-1 William Hill Scottish Cup draw with Aberdeen, but the pair will have to do battle all over again after Craig Brown's side snatched a late leveller through Niall McGinn.
Murphy will be key to Stuart McCall's side if they are to progress, and the ex-Scotland Under-21 star believes he now has the mentality to handle being in demand.
He said: "The speculation used to get to me a bit, but over the years I've had to deal with it and get used to it.
"I take it with a pinch of salt now, and I'll find out about anything when the club tell me about it. I'm enjoying just playing football at the moment, and I've not heard anything.
"We have to lift ourselves for the replay. We wanted to win it up here. We put in a good performance and managed to take the lead, but it's just one of those things. Football can be cruel sometimes.
"It's just one of those things. It's a ball into the box and Niall McGinn gets his head to it. If it landed anywhere else, either Lee Hollis would save it, or it goes wide."
He added: "I scored one like that against Hamilton a few years ago when Craig Brown was our manager.
"In fact, Craig told me to hit a lot more shots from outside the box because of that goal, and I think Saturday's was the first one I've scored since.
"He was great for my career. I owe him and Archie Knox a lot, and it's always a good game when the two teams meet."
The Dons will visit Fir Park on December 11 for the replay as two of the SPL's in-form sides go head-to-head once again.
And while boss McCall was frustrated not to already have the tie clinched, he praised this side's Pittodrie performance.
He said: "It was always going to be a tough game with two evenly-matched sides and as much as Craig has got a few injuries, they still had an experienced side out.
"In the second half, we gave them relatively few chances and we always looked a threat on the break. It's always sore to lose a goal as late as that especially after scoring such a terrific one ourselves.
"I'm really proud of the team as it was a tough one, especially with the players missing down the spine. I'm disappointed it's only a draw, but at least we're still in the hat."