GA TWIN LNDG ON RWY 2 WHILE ANOTHER ACFT IN TKOF POSITION RWY 20. GA TWIN DID NOT GET LNDG CLRNC. OPERATIONAL ERROR.

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WHILE OPERATING UNDER IFR AND RECEIVING AN APCH CLRNC STRAIGHT IN TO RWY 2; WE LANDED AND WERE ADVISED BY THE TWR THAT WE DID NOT HAVE A CLRNC TO LAND. OVER THE OM MY STUDENT; WHO WAS RECEIVING INSTRUMENT MULTI ENG TRNING; RPTED AND WAS TOLD TO IDENT (THE TWR HAS BRITE RADAR). WE CONDUCTED A SINGLE ENG APCH UNDER THE HOOD WHILE I MONITORED TWR FOR ANY OTHER LNDG INSTRUCTIONS. AT THE DECISION HEIGHT OF 200' I REMOVED THE HOOD; CHKED GEAR DOWN AND MONITORED THE FINAL APCH WHICH WAS A LITTLE LOW. AS WE CROSSED THE THRESHOLD AT ABOUT 10' I REALIZED CLRNC TO LAND HAD NOT BEEN RECEIVED AND TOO LATE TO REQUEST A CLRNC THAT THE CTLR SHOULD HAVE GIVEN. WHILE OUR NOSE GEAR WAS STILL IN THE AIR THE TWR OPERATOR STATED THAT WE HAD JUST LANDED W/O A CLRNC. MY STUDENT SAID; 'ROGER.' WE WERE THEN TOLD TO TAKE THE FIRST TXWY OFF THE RWY AND CONTACT GND CTL. I FEEL THE TWR SHOULD HAVE BEEN AWARE OF OUR STRAIGHT IN APCH GIVEN BY SAC APCH CTL. AS AN INSTR I SHOULD HAVE INSURED CLRNC WAS GIVEN BEFORE T/D. I FOUND OUT LATER THE TWR HAD POSITIONED AN ACFT IN POS AND HOLD TO DEPART ON RWY 20 OPP OUR LNDG. IT APPEARS THE TWR AND APCH CTL HAD NOT COORDINATED THEIR TFC. BY LNDG SHORT W/O A CLRNC; I FEEL I AVOIDED ANY CONFLICT. WHY DIDN'T THE TWR ISSUE LNDG INFO AFTER THE OM IF HE WANTED US TO DO OTHER THAN STRAIGHT IN? FAA PERSONNEL MET US AT TIE DOWN.