Last week's draw to Dumbarton signalled the end of Ray McKinnon's reign in charge of the Bairns.
A new management team has been ushered in with David McCracken and Lee Miller being made co-managers in the interim period.
Birthday boy Dixon, who scored and assisted in the 4-1 Cup win over the Rose, admits it's been hard for the players who were given the chance by McKinnon .
MORE: 'I loved it, I was kicking every ball,' - Miller revels in Falkirk managerial roleHe said: "It has been difficult, as a player when you enjoy working with a manager and you see them lose their job, it's that little bit harder.
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"All the boys in the changing room loved working with Ray and Darren and it is unfortunate.
"It's football, it's a result-based business the club have made that decision.
"We have to thank Darren and Ray for their work. They brought pretty much every player to the club so we have to thank them for that and we have to move on."
Falkirk are in fourth in League One, three points off the top.
Asked if he could put his finger on what ended up costing McKinnon his job, Dixon said "I think ultimately the draws did it.
"There's been huge expectation for us to blast the league that we're in but it's not going to be as simple as that.
"We are the scalp and teams are coming and making it hard for us so as players we need to figure a way out of getting through teams sitting in."
It's still early days but Dixon has been impressed by the impact new co-bosses McCracken and Miller have made.
He said: "They're very good, ex-team-mates that played together.
"They know how each other works personally and professionally.
"So far Cracks has taken defensive work and Lee's taken striker work and they've dovetailed very well.
"It's not just been one of them it's been both that have been putting the input in."