"It's only friendly banter like 'I'll see you soon' and Bainesy having a little bit of a joke," Baxter said.
"They're proper professionals. They wouldn't disrespect me or the club and say they're going to beat us.
"They really are top lads and the performances they put in for Everton show how good they are."
Baxter retains a strong affinity for a club where his appearance on the opening day of the 2008/09 season against Blackburn made him the youngest player in their history at 16 years and 191 days - a record that still stands today - and he relished an at times overwhelming occasion yesterday.
He said: "It was unbelievable, seeing so many of my old team-mates and my old manager who gave me the chance that I'm really grateful for, and what a manager he is.
"Instead of them being my team-mates and my manager they were the opposition, so it was a bit of an awkward one but I didn't half enjoy it."