The Toffees lost 1-0 at Manchester United on Sunday to slip to 12th in the Premier League table and leave them stranded, 15 points off a guaranteed Europa League spot and 11 points clear of relegation.
That mid-table obscurity means that the club have the bare minimum to play for in the remaining weeks of the league season, with only the 23 April Wembley date left as a bright spot.
Baines admitted that victory in that match, which will be against either Sunday's opponents or West Ham United, is the only way the players have of both making up for their underwhelming season and having something to shout about themselves at the end of the campaign.
The 31-year-old left-back told the Liverpool Echo: "I don’t think there is anyone expecting to have their name pencilled in for that game, but the motivation should be getting your name there.
"We want to win every time we go out to play and we’d like to go into that cup game with a few wins behind us. That’s our season in some respects now, it certainly is from the fans’ point of view and we’ve let them down a lot.
"It's our only way of making it up to them, to go on and have success in the cup now. You had the travelling fans there again on Sunday and they are amazing, they follow us wherever we go and generally they have seen us win a few games this season but unfortunately we weren’t able to give them the result or performance we wanted to."
Everton's fall from grace has been hard for the club's fans to handle this season, with a club used to finishing in or around the top six over the last 15 years staring down the barrel of a second consecutive campaign in the bottom half.
Baines suggested on Monday that a major reason for that poor form has been the lack of tangible chemistry in the Toffees team, and captain Phil Jagielka admitted that he can see no easy solution to the problems at Goodison Park.
Roberto Martinez's side face a hectic few weeks before they travel to Wembley, with a period of four league games in 11 days concluding with the Merseyside derby against Liverpool at Anfield just three days before the semi-final.