The left-back applauded the Slovakian's display in goal, with the shot stopper making several key saves to keep a clean sheet in the 2-0 victory over Manchester City
The England international praised the Slovakian's understated display, keeping the defending Premier League champions from equalising before Nikica Jelavic's late goal put the game out of reach for Roberto Mancini's men.
Baines conceded that it must have been tough returning to the side after a long period as understudy to the currently injured Tim Howard, but believes Mucha put in an excellent performance, making several key saves.
"It's never easy coming in when you have been out for such a long time. I'm sure it has been difficult for Jan, but he hasn't shown that," Baines told the club's official website.
"He's done really well for us and he kept us in the game. At 1-0 he made some great saves and on another day they could have equalised.
"He did well coming out, punching balls clear and taking a bit of the pressure off us.
"It was great to get the clean sheet as well. We haven't had as many as we would have liked, so I'm sure Jan will be delighted."
The left-back also praised Leon Osman's superb opening goal, putting the Toffees one goal up with his long range effort from 30 yards.
"It was a mis-hit," joked Baines, before stating: "It was brilliant.
"For all our pressure we needed a goal. If it hadn't come then they would have started to creep back into the game, but we dominated the first 45 minutes.
"The goal was much-needed and it was a great strike by Ossie [Osman]."
With David Moyes' men crashing out of the FA Cup to Wigan, Baines insisted the team had to bounce back and give a good performance.
The win over City now leaves them six points off Champions League qualification, with important games versus Arsenal, Tottenham, Liverpool and Chelsea still to play.
"It was important for us to show a response from last week and I think we did that," continued Baines.
"It was what we all needed, the club needed that. We wanted to get out of the blocks and really make it known that we were going to give everything we had.
"Obviously it took a bit of time to get over the Wigan game but towards the end of the week we started to focus on the City game and be more positive.
"We wanted to start the game in a positive manner and build on it, which we did."