Belgium midfielder Fellaini and England left-back Baines were this week subject of a £28million joint bid from Manchester United.
That offer was rejected as "derisory and insulting" by Goodison Park chiefs and Martinez is pleased with how the players have dealt with the situation.
Martinez said: "I couldn't be prouder of their professionalism and the way they have been behaving.
"They are two great assets of the football club. I think they realise what they have done in the past and they are very respectful towards that.
"In the same manner, the way we have dealt with things is very transparent, very clear. We always communicate whatever is going on with the players.
"They understand as well that the start of the season is a vital time for us.
"The only worry now is to prepare for the games and be as right as they can on the pitch.
"That has been important for the group. Football is a team sport and the behaviour of every player really matters. They have been a real example towards that."
Everton are now bracing themselves for a possible improved offer from United, whose manager David Moyes knows the pair well having only left the Merseyside club at the end of last season.
To have any chance of succeeding, United would clearly have to raise significantly what are believed to be £16million and £12million bids for Fellaini and Baines respectively.
Fellaini, 25, cost Everton £15million when he signed from Standard Liege in 2008 with 28-year-old Baines arriving from Wigan for £6million the previous year.
Yet even if the offers were to improve, Martinez insists there is still no temptation to sell.
The Spaniard said: "There is no temptation. In football you want to keep your best performers and that is where we are.
"You always get into a debate when there is a club that matches the valuation of a player. Then you need to make a decision.
"That has never been the case and where we are is we want to keep out most influential players and build from that.
"It has been well reported what the approach has been. We take it as a football compliment and move on. Now the focus has to be the games."
The issue has caused some consternation at boardroom level just months after United swooped on Goodison to recruit Moyes.
When asked what chairman Bill Kenwright's reaction had been, Martinez said: "A bit of everything really.
"When you make a massive investment on a player and he becomes one of the best performers in the club and you get a bid below what the club have invested, you are going to be angry, disappointed and hurt.
"Those are the emotions football brings but the chairman has always been in control of the situation.
"That gives you great stability and that is the way we will carry on doing things."
Martinez is one of several Barclays Premier League managers to have expressed their frustration that the summer transfer window remains open beyond the start of the season.
There have been calls for it to close before the first game but that would not mirror the situation in other European leagues.
Newcastle boss Alan Pardew was particularly angry after Arsenal submitted a bid for his player Yohan Cabaye hours before Monday's game at Manchester City.
Chelsea's Jose Mourinho and Swansea's Michael Laudrup have also said they would welcome an earlier closure.
Martinez said: "I have said it time after time, it is time for the football authorities to look into the situation.
"I think the window is getting out of hand and really affecting the values of the league and the human side of the players in a very unfair manner.
"It is about time we stopped the window or the official games in the middle of the window."
For now the transfer window does remain open and Martinez has not ruled out making further additions if the opportunity arises.
He said: "The squad is very good, we have a good balance.
"But in these situations you have to keep trying as hard as you can to add the right people.
"We will keep working hard to make sure we close the window in the best possible shape."