Murray was defeated 7-6 (5), 6-7 (4), 6-3, 6-0 by world number one Novak Djokovic in the Australian Open final, but Mauresmo believes his game showed improvement and his future looks promising.
Mauresmo said: "We have already made important progress – the little things are still to be worked on. There is not a lot of frustration. He gave his best. At the end we saw it wasn't enough. It's a bit hard, but that's how it is."
"Andy was a little bit timid when he had a break or led. Novak served really well – better than Andy. The two little things made the difference. But these have been two really good weeks compared to the end of last year.
"He has really succeeded in finding his level of play. Of course, there is a little disappointment after a loss in a final, which is normal. But we will all look back on where he has come from to where he is at now. There are still a few steps to climb before maybe holding a Grand Slam trophy again, but the gap is closing."