Slater, who is initially taking over from Jamie McKenzie on a temporary basis, previously bossed Lanark from February 2018 to October 2020 before quitting due to ongoing safety fears about attending games during the coronavirus crisis.
Slater said: "We are getting the squad built up with people I know and trust.
"I still don’t know why Ian and Declan were sitting in the house and Lanark had never approached them. But what’s happened in the past is nothing to do with me.
“I found that it certainly wasn’t the club I left or the playing squad I left so I knew I had to – probably first and foremost – try and stabilise it and hopefully pick them up a wee bit.”
When asked if he wants the Moor Park gaffer’s role on a permanent basis, Slater replied: “I signed three players on Sunday so I’m not going to ask those boys to commit if that’s not the case (that he wants job full-time).
"We’ll see what happens over the next few weeks and I’ll leave it up to George Reid (United president).
"Myself and Spike (interim assistant boss Cameron McNeish) suggested to the club that we would suggest the roles on an interim basis primarily to see what we had because if we felt we were going in there to help but couldn’t make a difference, there was no point.”
Slater’s first game back with United came on Saturday when they won 1-0 at local rivals Forth Wanderers in a friendly.
"We knew we could get up to Forth on Saturday with a relatively decent squad to go and perform,” he said.
"The boys did well. I was really pleased with the attitude, commitment and the way we played.
"It was a decent enough start with a bit of a threadbare squad and full of people coming in to help us out.
"The commitment that we’ve had from the boys on Saturday and in the training sessions has been excellent.
"We certainly still need to add to the playing squad, probably with a wee bit of experience. We still have a couple of injuries, to James Martin and Andrew Gilchrist.
"We’ve got quite a young squad but we’ve got good young talent there, local talent as well which I like.
"If I take my success at Carluke when we won the league and my success at Lanark when we won the league, using local talent and getting locals through the gate is a massive part of it and I think that’s been missing.
"We can only use so many. I’m not going to throw the young ones to the lions. We need to get experience.
"Although we have Gareth Halford, Mark Haddow, Cameron Lawson, James Martin, Ian Watt, I still think we have to add a wee bit of experience in certain areas to strengthen us for the campaign.”
United start their West of Scotland League Conference C campaign at home to Larkhall Thistle this Saturday, KO 2pm.
"I’m probably an old fashioned West Region Junior player and that’s what I liked,” Slater said.
"I’m not the biggest lover of the conferences so I’ll just play each game to win it and if we get the points we’ll be as high up the league as we can.
"For me the set-up now is a very easy game getting made difficult by rules and people that want to keep chopping and changing.
"It’s a very simple game so we’ll set out to get as many points as we can and where we end up, we end up.”
After this Saturday’s league opener against Larkhall, Lanark play their second league game at Glasgow Perthshire next Wednesday, KO 7.30pm.