The Soweto giants secured their third consecutive win in the Premier Soccer League (PSL) when they brushed aside Arrows 2-0 at FNB Stadium.
The German tactician also felt their game plan worked against a good counter-attacking side on the night.
"Just to mention it, I think in the PSL, Kaizer Chiefs was not able to lately in the history to win against Baroka FC, we did it. Now Golden Arrows is a very difficult opponent, they always have something to deliver, [on a] counter very good," Middendorp told SuperSport TV.
"We planned it, we discussed it, what's important we saw they had two games (in a week) and in the third game both teams will have an issue with the energy. You have to show a bit of a grown-up."
Middendorp gave the examples of Khama Billiat and Lazarous Kambole, who could not combine well to extend Chiefs' lead in the closing stages of the match.
"There's a lot of space for improvement on our side, we know it. In the last ten minutes, the lack of understanding [with] Khama [Billiat] and Lazarous [Kambole], the movement, the run - still not knowing what to do, where to go, which way I have to serve to assist the teammate but it's absolutely normal, still the beginning of the season," he added.
The former Free State Stars head coach went on to reveal the injuries suffered by Kgotso Moleko, Reeve Frosler, Siphosakhe Ntiya-Ntiya, George Maluleka and Samir Nurkovic are not serious.
"The injuries are not a big deal so far, if we (were) playing on Sunday Reeve Frosler would have been available, George Maluleka would have been available, (Siphosakhe) Ntiya-Ntiya would have been available, Kgotso Moleko would have been available," he said.
"At this moment we don't want to take a risk, really give them the time to recover and that's it. The beginning of the week next Monday, each and everybody, Samir Nurkovic (included) will be in and we prepare for the next game that is coming in."
The victory saw Chiefs maintain their lead at the top of the league standings and they are now five points above second-placed Bidvest Wits, who have two games in hand.
Amakhosi's next match is a PSL blockbuster against their Gauteng rivals Mamelodi Sundowns at Loftus Versfeld Stadium on Sunday, October 27.