"If we keep winning, keep him in charge, I see no reason why not," said Smith.
"I just hope the club don't use Eddie, until they find someone else, because of his loyalty.
"I've known Eddie since I was a kid and he would take the job if we were bottom and had no way of getting out of it because he loves Leeds United. That's the way it is.
"If he does do a good job then he deserves to stay in charge. For the time being he is enjoying being in charge and he's had to wait a long time to do it.
"Hopefully, his loyalty can be justified in our performances and the results we pick up.
"But he definitely has the backing of the players. Anyone who questioned that and then saw the game last Saturday will now realise everybody is 100% with him.
"The performance last Saturday was a proper Leeds performance.
"No disrespect to the people who have played this season, they've been in the team and done well.
"But with Eddie coming in, he wanted stability and he put a strong team out. When you looked round the dressing room there were a lot of leaders and characters.
"Most importantly, there were a lot of players who filled you with confidence that you could go out there and get a result and that's what we did.
"We went back to basics. Eddie said to the defenders, 'defend, do your job and get a clean sheet'. We wanted to be very solid and that's what we were.
"If you'd said before the game it would be 1-0, we'd have taken that rather than a 2-1 just to instil confidence because for the back four to get a clean sheet was vital.
"It's been well documented we've conceded too many goals, but the way we performed gave everyone confidence and the lift we needed.
"We can take a lot more positives out of the game than just the three points."