On-loan Rangers Zak Rudden netted in the 56th minute after home goalkeeper Ross Doohan spilled a Ross MacLean shot.
McKinnon gave starting debuts to five new signings, MacLean, Ian McShane, Mark Waddington, Ciaran McKenna and Paul Dixon and was glad to see immediate results.
He told Falkirk TV: "It was a big three points for us, worked extremely hard for them.
"We gambled, we wanted to freshen it up but it paid off.
"We played five new players massively lacking in match fitness aside from Ian McShane.
"We knew we would run out of steam in the second half but their attitude, resilience and desire to win the game was fantastic. We had to make a statement of intent, that we had to change things.
"I am very pleased but we need to keep improving."
Ian McCall's side remain three points behind leaders Ross County, who lost 1-0 against Morton on Friday, with Kerr Waddell getting the goal for the home side.
Partick Thistle earned a 1-1 draw at Dundee United but slipped to the bottom of the table.
Jags striker Kris Doolan headed the visitors in front after nine minutes but Fraser Fyvie levelled from the spot in the 62nd minute to leave Robbie Neilson's side three points behind Ayr United and six off the Staggies.
"It's a familiar feeling for us unfortunately," Jags manager Gary Caldwell told the club's official website.
"I thought we were superb in the first half; dominated the game and got our goal.
"We then should have added to it and put the game out of their reach but we didn't and paid for it in the second half.
"They came out and had a go. They were at home and only one down so that's to be expected but the lesson for us is that when we get good chances like we did, we need to take them because teams will punish you."
Dunfermline surrendered a two-goal lead to draw 2-2 against Alloa with Alan Trouten completing his double for the visitors in added time.
Aidan Keena, on loan from Hearts, opened the scoring after 18 minutes with a drive from 22 yards before Iain Flannigan put through his own goal 10 minutes later.
Trouten reduced the deficit four minutes into the second-half and the 33-year-old levelled in stoppage time with his 14th goal of the season.
Queen of the South came from behind with two goals in a minute against Inverness to win 2-1 and leapfrog Caley into fifth place.
Tom Walsh put the home side ahead in the 69th minute but Scott Mercer levelled with seven minutes remaining before prolific striker Stephen Dobbie quickly notched the winner with his 30th goal of the season.