Jason Dair's impressive first-half header gave the West Lothian men the all-important opening goal which proved to be the match winner.
"This is another sneaky three points, but at this stage of the season they are all welcome," he admitted.
"The quality of play was poor and it was that bad at times I turned to Archie (Knox, his assistant) and said 'this game will get football stopped'.
"Not many teams come here and win because Caley are a strong, physical side, so the players deserve a lot of credit. We are one win away from safety now and that's a great turnaround.
"I always knew I had the ability to do this job, but it's not about me and I think the players deserve the credit.
"The guys I brought in have done a great job and the rest of the team have pitched in with a massive effort."