David Moyes' side drew 0-0 away at top-four rivals Arsenal on Tuesday evening, leaving them four points adrift of Arsene Wenger's fourth-placed side with just five games of the campaign left to play.
|12/1||Everton are 12/1 with William Hill to finish in the top four
"We have been steady over the years. We have been shy of challenging for the Champions League places and are managing to edge our way closer," Baines told reporters.
"We have not had that big push in terms of giving the manager that backing to go and buy the players who would really put us right in the mix.
"It is one thing having it and obviously you have to spend it wisely.
"You have to get the right players and those who fit, so it would not be a given if we were to get a good amount of money, but it would definitely help."
With the club facing Sunderland away from home on Saturday, Baines said that while a top-four finish is now unlikely and out of the club's hands, the squad still have a chance of making it given their good form against those around them.
He added: "I think we are definitely the outsiders. If we are to make it then the others have to lose enough points. But we won’t give up on it. We will keep trying to win games. We have to go to Sunderland on Saturday and then we have a home game against Fulham.
"If we can get six points from those two games let’s see what everyone else does. We can try to keep up the pressure. You never know. We might just nick it. We have taken points off a lot of the teams who will finish in the Champions League positions.
"I don’t think anyone will particularly enjoy playing against us at any level.We have got a little bit of everything — the togetherness, work rate and spirit are inspirational at times."