The Toffees achieved a 7-0 success against Nottingham Forest in the third round on Wednesday.
Hat-trick hero Harrison Armstrong was a key reason for the win, but the entire team excelled.
“We’ve had that before – the lads coming to Goodison and making a little bit of a nervy start, but they got there in the end,” Baines told club media post-game.
“The goals before the break helped with that and, in the second half, we looked better in terms of what they know they are capable of. It’s a nice night of them.
“We just needed to find a balance early on. We were playing a little bit too direct too soon or too often which meant spaces on a big pitch, which makes you vulnerable in transition moments. I think we found a better balance between that and having control in the second half, whilst having some urgency and variety to the game.
“I spoke to Harrison before the game and told him not to put too much pressure on himself. Since I’ve known him as a first-year scholar, I could tell he's highly motivated and holds himself to a high standard. Regardless of dropping down the age group, a hat-trick at Goodison is a nice moment and him and his family would have enjoyed it.”