McCulloch was appointed permanent manager on a three-year deal, having been interim boss since 19 February.
"Some players where saying, 'how can we take you seriously when you're not the manager?'" McCulloch told BBC Scotland.
"But now it's confirmed I'll be pushing on to try and get the right players in for the club and the fans."
McCulloch, who says he is "delighted" and "ready for the challenge ahead", took charge of the team after Lee Clark left for Bury, and guided Kilmarnock to eighth place and Premiership safety last season.
He says there is a pressing need to add to his squad, with only around 10 senior players currently on contract at the club.
"We've got the youngest team in Britain so we need to try and bring in a little bit more experience," McCulloch said. "But along with that, some more young and hungry players.
"Other teams are making signings and getting word out there that they want certain players."
However with three Kilmarnock players involved with the Scotland under 20's side that beat Brazil at the Toulon Tournament, including Greg Taylor who scored the winner, he has plenty of confidence that the young players will deliver for him.
McCulloch also revealed he spoke to some supporters groups about the prospect of him becoming the manger on a permanent basis, "wanting to make sure they were happy".
"It's important to get backing from supporters, it's important that everyone is together, because we need to try and get into the community to get people back in to the stadium," McCulloch added.
Encouraging more fans through the turnstile is a priority for the new Kilmarnock manager at a club he believes is "a sleeping giant".
"We've an 18,000 all-seater stadium here and we're averaging 3,000 people a game, so we need to try and get everyone together, start connecting with the community and getting winning displays on the pitch," McCulloch said.
"I've been here as assistant manager for the last two and a half years, now it's straight into management so it came quicker than what I expected, but it's a challenge that I'm really looking forward to taking on."
Lee McCulloch admits Kilmarnock are "behind schedule" as they build for the new season.