CPR SMT ALT DEVIATION OVERSHOT DURING CLIMB.

Narrative

RECENTLY WENT TO A 2 PLT CREW. OUR COMPANY HIRED A LOW TIME PLT AND THIS IS THE FIRST TIME I HAVE WORKED IN A 2 PLT ENVIRONMENT. AS I AM USED TO FLYING SOLO; I AM HAVING A HARD TIME GETTING USED TO THE 2 PLT SYS. TAXIED OUT AT DAWN; 4 PLANES IN LINE FOR DEP. WE WERE ISSUED A VFR STAGE III DEP CLRNC; LEFT TURN 270 DEG 4500'. WE WERE CLRED FOR TKOF IMMEDIATELY BEHIND A MLG. AS THERE WERE OTHER PLANES WAITING; I DECIDED TO GET THE PLANE OFF THE RWY AS SOON AS POSSIBLE AND TO THE 270 DEG HDG TO AVOID ANY WAKE TURB. AS I WAS CONCENTRATING ON AVOIDING THE WAKE TURB; I LET THE COPLT HANDLE THE RADIOS AND DIDN'T LISTEN TO THEM DURING THE TKOF ROLL. TURNED TO 270 DEG AN AS I LEVELED AT 4500'; THE CTLR CAME ON AND SAID I WAS CLRED ONLY TO 4000'. COPLT IMMEDIATELY APOLOGIZED. CTLR SAID NO PROB; STAY AT 4500'. COPLT SAID CTLR NEVER SAID 4000'. CTLR SAID HE DID BUT PLT DIDN'T ACKNOWLEDGE. CTLR BLAMED HIMSELF FOR NOT FORCING PLT FOR ACKNOWLEDGEMENT. I BLAME MYSELF FOR NOT PAYING ATTN; PUTTING TOO MUCH TRUST IN A NEW COPLT AND NOT BEING USED TO A 2 PLT ENVIRONMENT. I AM SURE COPLT HEARD CLRNC BUT FORGOT IT OR IT DIDN'T SINK IN.