After the score finished 1-1 at the end of extra-time, Sunderland won the penalty shootout 3-0 on Saturday.
Garner told evertontv: “It's very disappointing. Hard to get back into the game. We were the better side in the second half, and we got the goal back and then extra-time, everyone was knackered.
“You know, we're down to the barebones with players and with all the injuries and lads off at AFCON, and all the suspensions and stuff.
"So, to stay in the game and take it into penalties was good, but it wasn’t good enough because me and the boys need to put the ball in the back of the net and there's no excuses for that.”
Garner also said: "Three games in a week is tough with a full squad, never mind half a squad. But like I said, I'm making no excuses. I think I've said in the past that we're all here for a reason.
“So, when the boys do play, and myself, we need to go out there and play more like the second half rather than the first half. We should be doing that from the off. And I'm pretty sure we would have had a different result if we did so."