Baines' brilliant last-gasp extra-time free-kick took the fourth round replay to the spot-kick lottery decided by Phil Neville's blast into the top corner.
It earned the Toffees a home tie with Reading in the last 16 and Baines recalled: "When I was away with England for the Denmark game I spoke to a couple of their lads, speaking to JT and telling him we might be a bit of a bogey team for them.
"Over the time I've been at the club we've ground out a good few draws against them and beat them at our place. We had a bit of a laugh about that.
"I was obviously trying to plant a bit of a seed of doubt and he was laughing it off. But we worked really hard. Our keeper kept us in it at times but for what we put into the game we deserved what we got."