The Goodison Park club are currently sixth in the Premier League table, four points adrift of Arsenal in fourth, following their 0-0 draw at Emirates Stadium on Tuesday evening.
Moyes, who is out of contract in the summer, admitted after the match that the Toffees may now need to win all of their remaining fixtures to have any chance of joining Europe's elite next term.
And England left-back Baines feels that the Scot's task of matching their Premier League rivals would be made easier if he was afforded greater backing in the transfer market.
He told reporters: "We've been steady over the years. We've been shy of challenging for the Champions League and are edging our way closer.
"We have not had that big push in terms of giving the manager that backing to buy the players that would put us in the mix.
"It is one thing having it and obviously you have to spend it wisely. You have to get the right players.
"So it would not be a given with a good amount of money but it would definitely help."