Norwich remain in the Championship's bottom three after dominating but failing to beat Burnley.
Jamie Cureton finished off Mark Fotheringham's pass from 12 yards to give the Canaries the lead.
But Steven Thompson squared the tie from close range after David Marshall could only parry Robbie Blake's shot.
Jason Shackell came closest to winning it for Norwich but his volley was kept out by goalkeeper Brian Jensen, who had an inspired game.
Norwich boss Bryan Gunn:
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"We have 12 cup finals left and we need to win more of them than we lose or draw to stay up.
"I think we will do it and I think the players believe that.
"They are very down because they have not taken all three points off a side going from promotion. That's the sort of attitude and character we need."
Burnley boss Owen Coyle: "I thought it would have been a travesty if we had won.
"Norwich put in a really good performance. I was pleased with the way we defended. When I first came here we would probably have lost that game.
"But we showed a lot of character, stood up to be counted, and came away with a hard-earned draw."
Norwich: Marshall, Otsemobor, Shackell, Doherty, Grounds, Croft, Clingan, Fotheringham, Hoolahan (Bertrand 83), Cureton (Daley 78), Cort (Killen 68). Subs Not Used: Nelson, Russell.
Goals: Cureton 20.
Burnley: Jensen, Williams, Duff, Caldwell, Jordan, Elliott (Eagles 62), Alexander, McCann, Blake (McDonald 63), Paterson, Thompson (Rodriguez 82). Subs Not Used: Penny, Gudjonsson.
Booked: Duff.
Goals: Thompson 36.
Att: 24,363
Ref: Kevin Friend (Leicestershire).
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