Former Fulham man McKinlay was appointed first-team coach last week, before stepping into the void left by departed head coach Oscar Garcia on Monday.
A Scottish international during his playing days, the 45-year-old has worked as a coach at Fulham, as well as assisting the management of the Northern Ireland international team, up until his resignation on Tuesday.
His first match in charge as a permanent head coach came on Tuesday evening, with Watford hosting Brentford at Vicarage Road, and McKinlay was grateful to his players for giving him the perfect start, courtesy of a 2-1 victory capped by a thunderous strike by Matej Vydra to win the tie.
Odion Ighalo opened the scoring in the first-half, converting a penalty at the second attempt, before Jonathan Douglas equalled the tie early in the second half. It was up to Vydra to claw the three points back for the Hertfordshire-based side, with his first-time volley powered into the back of the net.
Speaking to the official Watford website, McKinlay praised the players for the performance, despite the off-pitch madness that has surrounded the club in recent weeks.
He said: "All credit to the players this evening.
"It's great to get that first win on the board but I think it's more testament to them [the players] - and the existing staff here at the club - that they've been delivering results despite a fair bit of change since the start of the season.
"There's plenty of things I saw that will require fine-tuning over the coming weeks but what pleased me the most was the players' spirit and application. They really wanted to win that game and I thought our crowd got involved at a crucial time too, to give the players a nice lift.”
With the Hornets once again conceding a late goal at the weekend, losing a two-goal lead at Blackburn, McKinlay was delighted to see his side come away with the victory despite some intense endgame pressure.
The newly appointed coach added: "I'm sure that conceding a late goal on Saturday at Blackburn would have been in the minds of the lads at the back, yet for me I think that put some extra resilience within them towards the end of the match.
"There looked like a real determination to hold on for the win and, when you look at what happened near the end of the match, we could have scored one or two on the counter to kill things off.
"Overall I'm very pleased with parts of the performance. We're a long way from where I think we can get to, but it's a great start and good position to work from."