The Bluebirds have been knocking on the top-flight door for some time, with play-off heartache suffered in each of the last three seasons.
The Welsh outfit are hoping to avoid going down that route in 2012/13, with their efforts so far having taken them to the top of the Championship.
Malky Mackay's highly-fliers hold a 10-point lead over second-placed Leicester City and would appear to be well on course to hit their target.
There are, however, still 17 games to go and Conway concedes that there is still much work to be done.
He said: "Teams have slipped up in the past when looking like they were certain for promotion, so we have to ensure that nothing like that happens to us.
"We've another long trip now to Huddersfield which won't be easy, but our current form away from home is very good.
"Hopefully we can pick up another three points on Saturday with the right performance."
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