Baines told BBC Radio Merseyside: "We're not going to try and kid ourselves and pretend it doesn't matter too much now, because it does.
"We want to be higher up the table. The win over Birmingham will hopefully give us the springboard to do that in the coming weeks."
Everton's first league win was assured thanks to a stoppage-time header from midfielder Tim Cahill, with Baines providing the cross.
I couldn't have imagined facing the next couple of weeks still having not won
Leighton Baines
"The manager probably wasn't too happy with me being that far up the pitch and would rather I had stayed back," added Baines.
"I found myself in there and our first thought was to keep the ball in the corner, but the opportunity came for me to get the ball in the box.
"If it would have been anyone else I probably wouldn't have gone for it, but when you know Tim Cahill's in there, then you know there is always a chance of a goal.
"He was on the spot as always to seal the victory.
"It was vital for us to get off the mark.
"I couldn't have imagined facing the next couple of weeks still having not won and it would have been torture really in some ways."
Source: BBC Sport
Source: BBC Sport