The Argentine was able to provide cover for left-back Ryan Taylor from midfield which went a long way to shielding the Magpies back four who were brave in defending the constant set-piece threat from the Potters.
Gutierrez, who shared the Sky Sports Man of the Match award with hat-trick hero Demba Ba, said it was a great team effort to snuff out the home side who are so hard to beat at the Britannia Stadium.
"I think all the team worked hard in defence," he told Sky Sports 1.
"It was a hard game and the team defended really well in free-kicks against, corners against and throw-ins against. I think not just me but all the team did really well because not all the teams that come here take something.
"We won, we did a perfect game and I'm happy for them (my teammates).
"The pitch is small, they are really good with their set pieces so I think it's one of our best (games) in defence." And Gutierrez insists that the Magpies are not getting too carried away after their sixth win of the season, doubled with four draws, put them third on the Premier League table.
"We don't think where we are, we are thinking game-by-game," he added. "All the games in the Premier League are tough and difficult so now we have to focus on the next game.
"When we finish the league we see where we are but now we will take it game-by-game."