Amakhosi emerged with a 4-1 win with goals from Mduduzi Shabalala (4', 61'), Mfundo Vilakazi (73) and Flavio Silva (89), with Ayanda Lukhele (70) briefly firing his side back into the tie.
The result left Orbit in 12th place on the league standings with 13 points from 12 games, as Chiefs moved up to second with 22 points, from 11 games - level with leaders Mamelodi Sundowns.
Speaking after the game, Makhoye said on SuperSport: "We had a very good game plan, unfortunately we conceded an early goal and then we tried to contain them, especially in the first half, to make it to half time and rectify the mistakes we made.
"We created opportunities but we were not clinical, and even after we conceded a second goal from our own mistake, we kept on fighting, but then when we got one goal we became too desperate, because you want to equalise and you are committing numbers forward.
"Unfortunately we conceded a fourth goal and we lost, but it's water under the bridge and we prepare for the next one.
Orbit College are next in action against Stellenbosch at Olympia Park on 22 November.
Kaizer Chiefs interim co-head coach Cedric Kaze lauded his players following their 4-1 Betway Premiership victory over Orbit College at the FNB Stadium on Tuesday night.
Kaizer Chiefs moved up to second on the Betway Premiership standings with their win on Tuesday night, as new Chippa coach Vusumuzi Vilakazi picked up a point from his second game in charge.
Kaizer Motaung Jr. put on a brave face after Kaizer Chiefs were handed a tough draw in the CAF Confederation Cup.
Thabiso Monyane admits he is delighted to be back in action for Kaizer Chiefs after a month-long injury lay-off.
