O'Neill is leaving the job to take charge of Stoke City - though not before their Euros qualifying campaign is over.
"Everyone is very happy for him, what he has done at international level has been amazing," Evans said.
"He has been a constant through my international career, I've been working with him nearly eight years.
"He's always been that one manager to bounce off and has been incredible for my career and for a lot of the lads with Northern Ireland.
"We owe him a lot and I'm sure everyone sent him a congratulations text and it's even better to have him with us through the rest of the campaign."