It is unlikely; but, make sure that your new battery is not a dud or that the alternator has not failed. An automotive electrical service can load test the battery for you. Inspection of the voltmeter when the car is running will confirm whether it is working correctly - should be around 14.8 volts when running. If the alternator is good and you don't want to have your battery load tested, you can check to seek what the parasitic current is when the car is off. Remove the ground cable on the battery and connect an ammeter in between the battery negative post and the ground cable to measure the parasitic current. I have never measured mine; but, based on the rated amp hours of the battery and how long mine can last when parked (> 2 weeks) I expect that the normal parasitic current is less than 50 milliamps. If your parasitic current is in that range then your battery is bad or you have a charging system problem. If your parasitic current is significantly above 50 milliamps then you have an electrical problem.
If it does appear that you have an abnormally high parasitic current, start pulling fuses to see if you can isolate the source of the draw. The only legit parasitic loads that I can think of are the clock, the radio keep alive presets, the security system, (the keyless radio if you have retrofitted OEM keyless), and the keep alive for the ECU, ABS, TCS, SRS, EPS (if you have it) - anything with stored error codes.