However, he does believe changing a manager mid-season without a clear strategy has very few long-term benefits.
Solskjaer replaced Malky Mackay in January with the Bluebirds just a point above the bottom three but they head to Goodison Park this weekend inside the relegation zone, albeit on goal difference.
The former Manchester United striker had taken just seven points from his first nine matches, although they did secure a crucial win over bottom side Fulham last weekend.
Martinez believes the evidence shows short-term thinking does not pay off.
"It is difficult. It is very rare you get a real improvement for the long-term," he said.
"In the short term they sometimes get a positive reaction but a change rarely affects things in a good way for the long term.
"Sometimes we get those decisions. Overall you don't want to see those sort of changes and I personally don't believe the quick turnaround of a manager will give you long-term success unless you appoint the right man.
"It depends on every situation and every club has internal issues that they (should) know whether the decision will be right.
"But if you ask me nothing gives you more success in the long term than good stability and working with a real strategy to improve."
Martinez's most pressing issues are getting his side to bounce back from their FA Cup quarter-final exit at Arsenal last weekend and deciding when injured captain Phil Jagielka will be ready to return.
The Toffees boss has admitted he made a mistake in throwing Ross Barkley into January's Merseyside derby at Anfield just over three weeks after breaking a toe and he will not repeat the error by rushing back the midfielder's England team-mate.
Jagielka has missed the past two matches with a hamstring problem and Martinez is content to allow the 31-year-old to take his time coming back, especially with four matches in just 16 days starting this weekend.
"Phil is recovering well. Now it's a matter of assessing him day-by-day and seeing how quickly he can get back into playing," the manager told evertontv.
"Clearly it's important he is 100 per cent. I know he's a player who will at times put himself forward at only 90 per cent to help the team but with the amount of games we have - it's a nine-week period with 11 games - we need Phil and every player to be fully fit.
"Whenever Phil is 100 per cent he'll be able to help the team but we need to protect him a little bit and make sure he's not rushed back into playing too early, which could risk a further period out."
Midfielder Steven Pienaar's fitness will be looked at ahead of this weekend after limping off in the FA Cup quarter-final defeat at Arsenal.
"Stevie and a couple of others picked up knocks and bruises as you would expect from such a competitive and demanding game, but we're going to assess them over the next few days and we'll find the final extent.
"At the minute there doesn't seem anything to worry about."
- Sports & Recreation
- Phil Jagielka
- Malky Mackay