With 54 minutes on the clock, the Luton forward showed great movement in the box to peel off his defender and head past Whites keeper Kiko Casilla for a sixth of the season.
It was his first strike in nine appearances for club and country, with his last coming against Blackburn Rovers on September 28.
On the input that Jones, himself a forward in his playing days, had during his barren run, Collins said: “If you ask any striker if they go through a goal drought, they’re going to get frustrated.
"That was the case and me and the gaffer did speak.
"He just filled me with confidence, we had a really good chat about it, which will obviously stay private between us.
"But he still believes in me, still sticks by me and plays me, he knew I'd come out the other side and thankfully Saturday I did.
“It’s been a long run without a goal, but the quality of the league, the results not going well and the competition you’re coming up against (is tough).
"To score a goal is great, but I was really disappointed it didn’t count for much.”
During the sequence, Collins has played wide and deeper than he had during his previous two years with the Hatters, none more so than the 3-0 defeat at Reading recently, when he found himself defending Royals’ attacks by his own byline at times.
On his different roles this term, the forward, who now has 51 goals in 110 games, said: “I’m the type of player that I don’t really care where I play as long as I’m on the pitch to help the team.
"The gaffer away from home that day felt like I could do a job off the ball, because we thought they’d have a lot of the ball.
"Obviously I didn't get many chances, but I thought for the team, I did okay.
"I do want to be up front and scoring the goals, but in this league we’re going to come up against a lot bigger opposition and people that keep the ball a lot better.
"So if the gaffer wants me to do a different role for the team then that’s fine by me.
“It’s down to me to get in the box and make sure I’m on the end of those chances, which is a challenge for me.
"But if I’m on the pitch, I’m playing and that makes me happy, so I’ll just get on with it.”
Since winning promotion last season to the Championship, a level Collins hadn’t played in his career, he knows it has been a far more difficult proposition to the standard he was used to.
He said: “You do get fewer chances and you’ve got to be more ruthless when you get your chances, because you might only get one a game.
"That’s been what’s wrong with me the last few weeks as I’ve been getting those chances and not putting them away.
"So I've been working hard on it in training and luckily for me Saturday it went in.”
Even though he hadn't been scoring, Collins had come close on numerous occasions, denied by a wonderful save from Millwall keeper Bart Bialkowski, hitting the post at Birmingham, while also missing presentable chances at St Andrews, Fulham and the Madejski Stadium, with Bristol City stopper Dan Bentley repelling another of his efforts too.
Collins could take confidence from the fact he had a goal threat, adding: "That's the important hing, I was still getting the chances.
"If you're a striker and you're not getting the chance, that's when you need to worry, but I was still getting the chances, I just wasn't executing them.
"That means you've just got to keep going and one will fall for you.”