Everton assistant boss Alan Irvine says Yakubu Aiyegbeni accepted his axing for Saturday's defeat at Aston Villa.
That resulted in Baines remonstrating with Yakubu for his lack of effort.
The 24-year-old then trained on Monday with a group of players who had not been involved in the defeat to Villa.
Now it remains to be seen whether Moyes will restore the former Middlesbrough striker to the side for Wednesday's Carling Cup third-round tie against Sheffield Wednesday at Hillsborough.
At least from Irvine's point of view, Yakubu has not let his shoulders drop or taken the criticism to heart.
"He has responded really well to being left out, and that's what you hope for from players," added Irvine.
"We are a hard-working team, and we need all of our players to do a very committed and totally honest job when they are out there.
"We also ask them to do not only their own job, but to help other people out as well.
"I'm sure Yak will fend to that. He seems a great lad."
Irvine also believes left-back Baines was perfectly entitled to vent his frustration at Yakubu.
"It's the way it should be, and it's the way it's always been," added Irvine.
"The best teams have always been able to tell each other what they think.
"Everyone talks about team spirit, well team spirit isn't about always being everybody's friend, or telling them the good things.
"It's about being able to tell them what you think and what they need to do to help you, and people have to accept it and not take it as being something personal.
"When people can argue, get on with things and still be friends, that's when you know you've really great spirit.
"And from what I've seen he (Yakubu) has not taken it personally at all. He has come in smiling.
"He trained in a very small group of lads yesterday of lads who hadn't played, and was terrific.
"While today he has come in with a smile on his face and there has been absolutely no problem."
