The Rockets lost 3-0 to Kaizer Chiefs at the FNB Stadium in their last 16 clash on Tuesday.
With the club struggling in the Betway Premiership in 13th place with just six points from their opening eight games, their cup exit means that Galaxy can refocus their efforts.
"I think the most important thing for us now is the league. Maybe this exit was a blessing in disguise to concentrate more on the league because that's what matters for us," Mtsweni said in the Sowetan.
"I don't want to say this, but I think it was a blessing in disguise. Obviously we came here to win, but after seeing this performance, I think it was good for us to be eliminated, so that we can concentrate on the real deal."
Mtsweni took charge of the team following the exit of Bernard Parker and oversaw a 3-0 defeat to Orlando Pirates before their cup defeat.
"Today we saw who's ready for this level and who's not ready for this level. I can't say it's the fitness because we prepared well. Only the players can say what's the problem," the coach explained.
"We brought in an experienced player [Zulu] and took him off again because he didn't come to the party.
"It was evident from the first half that things weren't going our way. We didn't look like a team that wanted to win. We kept on playing negative passes, and it was very much concerning for me."
Next up for Galaxy is a trip to face Polokwane City on Saturday.