It has been a season of ups and downs for the Ayrshire side but Saturday's success over Motherwell, albeit relatively undeserved, leaves them just a point off the top six.
And Dayton, the victim of both Fraser Kerr and Keith Lasley's red card-earning kicks, is calling for a steady run of results.
"We have found it hard because we lost some important players in the transfer window but we need to find our feet and try to push on," he said.
"We got a bit of luck against Motherwell but need to take confidence from the result.
"There is only a point now between us and the three teams above us, so if we put a sequence of results together then we could get ourselves into a decent position.
"We said at the start of the season we'd like to make it into the top six and it is still within our own hands to do that."
Killie are back in action on Wednesday night when they head to Inverness to take on Terry Butcher's side.
The Highlanders lost to Celtic at the weekend, the latest in a poor sequence of results for the second-placed club.
But Dayton is bracing himself for a backlash.
He said: "They have got themselves up to second, so we know that it will be a hard night.
"Whenever you lose a game you are always looking to the next opportunity to put it right and that's how they'll view the game against us.
"But we want to start pushing ourselves up the table. We are capable of a higher position."