Anichebe, 23, came off the bench to grab Everton's equaliser, his second goal of 2012, but the Nigerian is keen to avoid the injuries that have plagued his career thus far.
"I think we deserved more out the game," Anichebe told Sky Sports News. "Our two central defenders were doing really well then they got the goal.
"Then we changed and got the goal back, we worked hard to get back in the game. A draw is better than the loss, but we would have liked the win.
"I'm really pleased but the main thing for me is to keep staying on the pitch, goal or no goal, and just keep playing. I don't want to be back in the treatment room."
However, the prospect of picking up another injury still fills the striker with fear.
Speaking of an incident shortly after his goal, Anichebe said: "Sometimes I'm a bit stupid and try to keep the ball in when it's impossible and my knee buckled.
"But I think there was just a fear because I have done stuff in the past so I always fear for the worst.
"I just thank God there wasn't anything serious and we can now kick on as a team."
Anichebe joined Everton in 2006 and has since scored just 15 goals in his 125 appearances for the club.