The on-loan Swansea player helped the Dons consolidate second place in the Scottish Premiership with a late 1-0 victory over Hibernian at Pittodrie on Friday night.
Tate told RedTV: "For a defender it doesn't really get much better than a win and a clean sheet.
"I don't think we were ever really in any danger of conceding goals. I don't think Jamie (Langfield) had many top saves to make. I remember one from a long-range free-kick and that was probably about it.
"So, not just from a back four or a personal point view, from a team point of view it was a good defensive display.
"For about 80 minutes I was okay and then I started cramping up. But that's one of the things that will come with game time.
"I enjoyed it. I played okay but I can do better."
Tate's enjoyment was helped by Willo Flood's spectacular 25-yard winner in the closing stages.
"It was a great goal," the 31-year-old said.
"It was one of them that, as soon as he has hit it, and you know it's on target, you know the keeper has no chance because he has hit it so well."
Tate was reluctant to make comparisons between the Scottish Premiership and Barclays Premier League.
Tate, who was on loan at Yeovil and Leeds last season, said: "Obviously it's a bit different and a bit slower. But I still enjoyed it all the same. I'm not here to judge Scottish football against English football.
"I'm here to play football and enjoy it and hopefully be successful with the club. What comes off the back of that, who knows."
Hibs suffered only their second defeat in 10 games under Terry Butcher and Maurice Malpas but the Easter Road manager hopes their below-par display in possession and attacking play will serve as a useful lesson.
Butcher told HibernianTV: "You learn more from a defeat than you do a victory. The players were doing things I don't want them to do and I have never seen them do before.
"It's not because they don't agree with what we say, it's just because they are so eager and discipline goes out the window, and they try things that they think might work.
"It's a harsh lesson but we will learn from it. We will be better for this defeat."
Winger Alex Harris made a late comeback from the broken foot that has kept him out since August while Butcher confirmed several departures.
Former Hearts right-back Fraser Mullen has left the club to sign for Raith Rovers, striker Ross Caldwell has joined Alloa on loan until the end of the season while his fellow 20-year-old David Gold has signed for Cowdenbeath in a similar deal.