The Toffees paid tribute to the 96 fans who died as a result of the disaster in 1989 before the game on Monday evening, as well as the families who have fought for justice since.
Baines' father, a Liverpool fan, was in the Leppings Lane end on the day of the FA Cup semi-final but survived the incident.
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"What our club did before the game was a nice touch. Hopefully now people can move forward and hopefully they have gained some of the closure they have needed.
"It is hard to relate our game with something so huge as Hillsborough, but it was important for Everton as a club to show their respect to the families."
Baines put Everton ahead against Newcastle but Demba Ba cancelled out both the left-back's strike and Victor Anichebe's 88th minute goal to earn the visitors a point.
The 27-year-old was left disappointed at his side's defensive display and felt that the Senegalese striker's two goals were both preventable.
"What is disappointing is Newcastle didn't do anything special, they didn't have any real play, they just played very direct got pretty much most of their joy from long balls and got their goals that way," Baines added.
"We have got to be able to deal with stuff like that. They were pumping balls up time after time in the second half and Demba Ba gave them that bit more physical presence, but you must be able to defend that.
"It's disappointing we didn't and couldn't hang on when Victor scored. Newcastle have good players up front and are strong and quick, but we've got to be able to deal with that more often than we did on Monday.
"It's unusual for us not to see out the game. It's very un-Everton like. It's disappointing that we haven't been done by a wonder goal or a magic piece of play. It was straightforward stuff. We feel both goals were preventable."
Everton had three goals disallowed in the match and replays showed that two of them should have stood. Marouane Fellaini's second-half goal was wrongly ruled out for offside before the officials waved play on when Anichebe's header crossed the line.
Baines, while frustrated, was keen to recognise the wider significance of the evening on Merseyside, however.
"Yes, it's disappointing - we scored five goals against Newcastle, four good ones, and we only got awarded two of them," he reflected. "That's disappointing.
"But you think of what happened at Hillsborough and it really does mean nothing in comparison."