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The Leicester defender is confident his country will remain on track despite O'Neill joining Stoke.
But the manager will still take their final Euro 2020 qualifiers against Holland on Saturday and Germany next week and any play-off in March.
Motherwell boss Stephen Robinson is favourite for the job and Evans expects the next appointment to be correct.
"It allows the IFA to take their time now, I'm sure they'll pick the right man for the job," he said.
"They made an unbelievable appointment in Michael and he's spoken before about how they gave him time and backed him during a time of transition and difficulty at the start.
"What the IFA have done over the last few years has been first class and I'm sure they'll pick the right man."
O'Neill was appointed in December 2011 and took Northern Ireland to their first major tournament in 30 years when they reached Euro 2016, making the second round.
Last year O'Neill turned down the Scotland job but replaced Nathan Jones at Stoke last week, winning his first game 4-2 at Barnsley on Saturday.
It lifted Stoke off the bottom of the Sky Bet Championship and Evans revealed his respect for his international boss.
"Everyone is very happy for him, what he has done at international level has been amazing," he 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."
According to The Sun, the Charlton boss has impressed some of Cardiff's leading figures and they see him as a leading option to replace the veteran manager.
The former Newcastle United midfielder took over at Charlton in 2018 and he has since won almost half of his games in charge, guiding the troubled Addicks to promotion from League One last season.
Despite the off-field ownership issues and lack of funds at his disposal, the 42-year-old has seen the South London club adapt well to life back in the Championship and they are currently one point and three places above Cardiff.body check tags ::
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