"We're just glad the club took the stance they did and we've been able to keep him," Baines told Everton's official website.
"It has been relentless, particularly for John. Seeing him first-hand on a daily basis, it's been difficult for him to deal with. He's still a young lad.
"John knows how to play football - he's being doing it all his life - (but) he hasn't had to cope with situations like this before."
Stones picked up his fifth England cap last weekend in the Three Lions' 6-0 win over San Marino and is expected to play against Switzerland at Wembley tonight (7.45pm).
He is also set to face Jose Mourinho's men on Merseyside in Saturday's 12.45pm kick off in the Premier League.
"It's John who has to pick himself up now, dust himself down and move forward," the England left-back added.
John Stones - Spotlight on
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"I think there's a misconception sometimes - people think that when a footballer hands in a transfer request they do it and go off and play a game of golf or whatever.
"But it's actually been such a tough thing and, as a young lad, you do lean on other people a bit more for advice at these times.
"I think the true reflection of John has been shown on the pitch - he's conducted himself brilliantly in the dressing room and he's performed well in all the games."