The Toffees produced a dramatic comeback victory over Arsenal on Monday, their first league win since September.
"We pushed each other hard all week in training," Coleman told the club's website.
"We understand the ups and downs of this profession.
"We had to fight and we had to earn the win – you don't just earn it during the match, you earn it during the week.
"We did that and got three points.
"That is all it was – three points – but they felt very important.
"The fans wanted a reaction from us after the derby and they got it.
"It is so important, going forward, knowing what we are capable of if we work together as a team.
"That starts on the training pitch, every single day, and we got the result we needed.
"We have quality, we've known that from the beginning. Injuries are part and parcel of this league, you have to deal with them.
"But we are getting players back. We're missing our striker, our main goalscorer, but we are definitely in a better place than we were three or four weeks ago."
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