Saints are currently on an 11-game run without a win in all competitions and are two points adrift at the foot of the cinch Premiership.
However, Davidson - who won a cup double last term - has a close bond with the chairman and has been allowed to bring in several new faces this month, including Dan Cleary, Nadir Ciftci, John Mahon, Tony Gallacher, Cammy MacPherson and Melker Hallberg, who joined on Friday following his exit from Hibernian.
He said: "I know not all managers would still be here (given the run the team has been on). Myself and the chairman have honest conversations about where we are and what we think, and he's been absolutely fantastic. Both of us have a passion for the club and want to succeed.
"We lost our best players on the last day of the last transfer window but hopefully this turns out to be a much better window. There are a few players struggling with injury as well, so we need to make sure the squad is strong enough to cope with that.
"The chairman is obviously supporting me and my staff and wants us to do well, so that's good news. I think you can see with the players we're trying to bring in that he is backing me. He believes we're doing the right thing.
"It's important to have a strong relationship with your chairman otherwise I probably wouldn't be sitting here speaking to you just now."
Davidson, in only his second season as a manager, feels the adversity he has faced in recent months has improved him as a boss.
He said: "It's the biggest challenge I've faced in my football career, without a doubt.
"I find it difficult when we're not getting results. I'm going through every little thing to try and work out how to make us better.
"My wife will tell you I'm an absolute nightmare at the moment, sitting at home on my laptop watching games of football, watching players and having no social skills whatsoever.
"But I'm probably a better manager now than I was six months ago, and that's my honest opinion. We had a tough time last season and came through it to do something incredible.
"We started this season well, especially in Europe, and we've obviously had this dip but I've learned a lot about how to deal with certain things and I believe I'm a better manager for it.
"Hopefully the results can get better and we go onwards and upwards."
Hallberg could make his debut away to Aberdeen on Saturday but Ciftci is out as he awaits scan results following an injury sustained against Dundee on Wednesday.
Davidson is still hopeful of further strengthening his squad, and said: "I'm still trying to get another attacking player in but I think everyone's chasing an attacker at the moment. Hopefully we can get one in and there might be another one on top of that."