Houston had been in talks with the Tannadice side over a new deal, but at a joint press conference with chairman Stephen Thompson on Thursday, he revealed he has decided against extending his contract on reduced terms.
Speculation began immediately with regards who would succeed the former Scotland assistant, with ex-United skipper Derek McInnes, who recently departed Bristol City, installed as favourite by one bookmaker.
Killie boss Shiels, though, insists the United players are too professional to be affected and will also be playing to impress their future boss, whoever it may be, when the Clydesdale Bank Premier League resumes after the winter break.
He said: "I think Peter has done magnificent there, but it won't affect the players because they have quality players right through the team.
"So I can't see it having an adverse impact on the team, they are too professional. I can see it having a type of 'let's play for our places because there could be a new manager who comes in who might not like us'.
"Dundee United played really well against us at Tannadice in the last game when it was 3-3.
"We were 2-0 up and 3-1, but they came back and got a goal at the end of the game and thoroughly deserved it. They have a fantastic team and great players."