A solitary Charlie Mulgrew goal in the first half gave the former Celtic boss a win in his first match in charge in a friendly at Pittodrie last night.
It was a positive start to the reign and gave the national team a much-needed lift ahead of their World Cup qualifiers next month.
However, Wigan forward Maloney, who played superbly in the first 45 minutes, believes Scotland can do much better in their meetings with Wales and Serbia.
He said: "Each manager has his own thoughts on how he wants the team to play. In the last few days the gaffer has tried to put those across to us.
"At times against Estonia I think we did what he wanted us to. There were some good parts to our play and he told us he was reasonably happy in the dressing room afterwards.
"But having said that, there is still work to do. The style which he is trying to get across has to be fine-tuned and polished and I am sure it will be in the future.
"The pitch wasn't conducive to the passing football he wanted us to play. That is the main thing that I think he wants to work on with us.
"We defended well at times. The back four was pretty good and it was pleasing for us to keep a clean sheet. It gives us plenty to build on when we meet up again next month."
Celtic left-back Mulgrew scored his first goal for his country just before half-time after a well-worked free-kick taken by Stoke midfielder Charlie Adam.
Maloney revealed that it was a ploy the players had discussed before the game – and one he had seen used by Strachan when he worked with him in the past.
He said: "Charlie took his goal beautifully. It was a set-piece that a couple of players had talked about. We haven't had that much time together on the training ground, but we managed to pull it off.
"I have seen it used under this manager (Strachan) in previous teams. It doesn't always come off in competitive match situations, but it worked well against Estonia."
Former Rangers winger Chris Burke returned to the international fold for the first time in seven years and posed a real threat during his time on the park in the first half. Maloney reckoned he was Scotland's best player and believes he can play a key role for the side in their Group A double-header next month.
He stated: "In the first 20 minutes Burkey was outstanding, just brilliant. I hadn't played with him for a while, but I know what a good player he is and I wasn't surprised with how he performed.
"It has been a while since he has been involved with Scotland, but he has been playing very well down in England for a long time. We all know what he is capable of. I was happy for him.
"One against one, he can go by players. When you have somebody like that in your team it is a big plus. He definitely poses a threat when he gets on the ball.
"But we have a few guys who can do that. Robert Snodgrass, for example, came on after half-time and did something very similar to him. Matt Phillips and James Forrest, who weren't involved, are in the same mould."