The Urban Warriors crashed out of the Nedbank Cup to the Black Jaguars yesterday 4-3 on penalties after a 2-2 draw in 120 minutes.
Nxumalo scored during regular time but missed his penalty in the shootout while Erick Chipeta's spot-kick bounced back off the underside of the crossbar.
This means Ajax, who won five out of six games before the end of 2016, are winless in 2017 stretching to six games in all competitions.
Nxumalo, who previously worked with KwaDukuza coach Thami Ngubani in the development structures in Durban, says losing to lower division opposition was not something they expected.
“I’d say we didn't expect to lose and we feel embarrassed,” Nxumalo tells KickOff.com.
“Yes, I scored two goals but it's bittersweet because the team lost but I think scoring today will also help me going forward and also to the next game.”
Nxumalo played down an incident in the second half of extra time when he was manhandled by a KwaDukuza player as he was going clean through on goal and the player only received a yellow card, following a defense-splitting pass from Abel Mabaso.
He was clean through to face KwaDukuza goalkeeper Nimrode Tsengwa before the infringement and coach Menzo was furious at referee Bafana Mosia for not showing red.
“But the game is finished now and I can't dwell on it, what happened happened and it's finished,” adds Nxumalo.
“Having said that, these KwaDukuza boys played well and they were up for the fight. They always say when you play a side from a lower division you don't have to underestimate them and I can safely say that we did underestimate them, we didn't start in the way we wanted to start.”
Ajax, who are 12th on the Absa Premiership table with 21 points from 20 matches, will switch their focus when they host Free State Stars at Athlone Stadium on Friday.