A CRJ-100 FLT CREW FLEW THROUGH THEIR ASSIGNED ALT IN CLB; CAPT CITES FATIGUE AS A LIKELY FACTOR.

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I HAD BEEN ON DUTY FOR ABOUT 10 HRS THE DAY OF THIS EVENT. THE PREVIOUS DAY I HAD FLOWN ABOUT 8 HRS WITH A VERY SHORT OVERNIGHT FOLLOWED BY 8.25 HRS OF FLYING THE DAY OF THIS EVENT. THIS HAD LED ME TO BE TIRED AND FATIGUED TO SAY THE LEAST. UPON RETURNING TO CVG; I WAS DISPLACED TO DO THIS OUT AND BACK. THIS EXTENDED MY ALREADY LONG DUTY DAY EVEN LONGER. IT WAS THE FIRST TIME THE FO AND I HAD FLOWN TOGETHER. UPON CLBING OUT OF CVG ON THE ROCKT2 DEP; WE SWITCHED TO ZID AND CHKED IN. WE WERE CLBING OUT OF FL198 WHEN ATC SAID MAINTAIN FL190. I; BEING THE PNF; SAID WE WERE LEAVING FL198 AND ATC SAID; OK; MAINTAIN FL200. I IMMEDIATELY PUSHED THE ALT BUTTON ON THE FLT CTL PANEL TO STOP AT FL200 AND WE LEVELED THERE. ATC SAID; 'WHAT ALT WERE YOU CLBING TO?' THE FO AND I LOOKED AT EACH OTHER WITH FL230 SET IN THE ALT PRESELECT AND SAID FL230. ATC SAID 'CLB TO FL260' (RIGHT ALT FOR DIRECTION) AND SAID 'YOU WERE SUPPOSED TO STOP AT FL190.' I COULD HAVE SWORN WHEN I CHKED IN INITIALLY WE WERE GIVEN FL230. I TOLD ATC THAT I BELIEVE I READ BACK FL230 WHEN WE WERE GIVEN AN ALT UPON CHK-IN. WE LOOKED AT OUR FLT PLAN AND IT SAID FL190. I HONESTLY DON'T KNOW OR REMEMBER WHAT ALT WE WERE GIVEN. THE FO AND I DO NOT REMEMBER SETTING OR CONFIRMING THIS ALT. NO OTHER ACFT WERE NEAR AND ATC NEVER SAID ANYTHING ELSE ABOUT THE DEV. THIS IS THE FIRST TIME THIS HAS HAPPENED TO ME. I HAVE NEVER USED AN EVENT FORM; THIS IS THE FIRST. I DO KNOW THAT FATIGUE PLAYED A PART IN THIS; IF IN FACT IT WAS OUR FAULT. I HAD FLOWN 22 HRS 5 MINS IN 3 DAYS WITH LITTLE OR NO REST IN THE LAST 2 DAYS OF THE TRIP. I BRIEFED THE FO IN MY INITIAL BRIEF I WAS EXHAUSTED AND TO KEEP AN EYE ON ME. WE BOTH DON'T KNOW NOR CAN WE REMEMBER; IF ATC ISSUED US FL190 OR FL230. I MAY HAVE READ BACK FL190 AND THEN SET IN FL230 IN THE ALT PRE-SELECTOR. I DON'T REMEMBER BECAUSE I WAS TIRED. SUPPLEMENTAL INFO FROM ACN 706606: THE CREW WAS QUERIED BY ATC OF OUR ALT. THE ALT PRE-SELECTOR WAS SET AT FL230. ATC TOLD US TO MAINTAIN FL190. WE WERE ALREADY THROUGH FL190. THE CTLR THEN GAVE US FL200. THE CONFUSION WAS THAT WE WERE NOT SURE THAT ATC HAD GIVEN US FL230. IN RETROSPECT; I DIDN'T RECALL SETTING FL230. IN HINDSIGHT; I SHOULD HAVE ASKED ATC AGAIN BECAUSE OF OUR FILED ALT.