The former Bolton midfielder was given a straight red card for a mistimed lunge at the Toffees's Nigerian forward, with the striker hobbling on for several minutes before being replaced shortly before half-time.
Anichebe, who was initially concerned that his leg was broken following the tackle, will undergo tests on the injury on Monday, but says he is hopeful the damage is not as bad as first feared.
"I've never felt as much pain in my life," he told evertonTV. "I thought I'd broken my leg. I couldn't even look down, to be fair. It was a terrible tackle but I don't think he really meant it, he came and said sorry. But what can you do?
"I felt so much pain. Now it's not too bad. It's not as bad as I first thought anyway, but I'm feeling a bit of pain in my knee and the back of my calf and down my shin so we'll see how it is.
"I've always thought to myself I'll never get injured for a long period of time. When it happened I thought, that's me, that's my time, but luckily I've got strong legs anyway, and if that was anyone else, their leg would have snapped in two.
"I suppose I'm lucky to come out not as bad anyway, so I'll get a scan on Monday and see how it is. Hopefully everything is all right."
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