Walsh scored a chip from the half-way line in a 2-0 win for Everton's U18 side over Derby County last month.
And Martinez believes that the stunning strike highlights the special talent that the youngster has.
“The technique of that action is not easy to execute,” Martinez said. “Liam’s vision is quite special. On top of that he was arrogant enough to think that he could score from that distance.
“We always encourage our players to be free, to enjoy being creative, and clearly when you have talented players like Liam Walsh, you produce moments like that.”
Walsh is sure to be buoyed by Martinez’s words, which suggest that the club have very high hopes for him in the future.
Indeed, Martinez went on to further state how excited he was about the current crop of youngsters breaking through at Goodison Park.
“I am really excited about this crop of youngsters,” he added. “It is not just a group of players competing in their league, they are players have been moved up to the Under-21s.
“It is very important to have good players but it is even more exciting to have youngsters with the quality that we have underneath. Now we want to see them grow and see where they can take us.”
Martinez has shown his faith in Everton’s youth system during his time at the club, with a number of prospects being handed first-team chances.
The likes of Ross Barkley, Brendan Galloway and Tyias Browning have all received regular competitive action at Everton this season after rising through their academy system, and the club’s youngsters will be hoping to follow in their footsteps in the near future.