The Argentine shot-stopper, who arrived last week in a £20million deal from Arsenal, helped his new club make a winning start to their Premier League season by keeping out John Lundstram’s first-half penalty.
Ezri Konsa then got the only goal in the second half as Villa edged past a Blades team who played most of the match a man down, after John Egan was sent off on 12 minutes.
Martinez said: “Keeping a clean sheet and getting the three points - what a start.
“I didn't even know where to dive to be honest. Obviously penalties are luck and at the end of the day I just follow my instincts.
“All goalies work and watch videos on watching Sheffield United and their strengths but like I said it is just instincts.
“It feels great, it was like scoring a hat-trick for me. Saving a penalty and keeping the clean sheet for me is the best game I could ever play.”
Martinez’s performance won plaudits from boss Smith, who said: “Emi is calm, assured and has a great personality and character. He knows what it is like to play for a big club.
“He made a really good save from the penalty and we believe will be a really good signing for us.”
Villa’s victory came hours after Tyrone Mings became the second player in the space of a week, after skipper Jack Grealish, to sign a new contract.
The England international has agreed an extension on significantly improved terms through to 2024.
Smith said: “Tyrone is a really key member of the team. We are happy he wanted to commit again.
“We said Jack signing a new deal was a statement of intent from our owners in terms of where we want to go to.
“I thought he played well. It looked as though he might have a heading bonus in his new deal, the amount he won.”
The boss continued: “I thought we showed a bit of rustiness but overall I thought we looked a fit team.
“There was certainly a freshness about us and we started the game well. We were camped in there half for long periods.
“I think we will be OK this season. There is certainly more to come from us but it was a satisfying start.”