Hi Sooraj243, Sony did explain in their blog that we might experience a few glitches such as these and lets face it, Android 4.1 does correct most of these lags, but we poor blokes stuck with ICS have to manage somehow. Anyway, try to switch off your phone every night and switch it on the next morning, the speed of your phone should have improved somewhat. Also, do a hard reset of your phone as some files might have been left over during the update to ICS.
Btw, I have the same phone as you and faced the same problems. So, I installed a custom ROM on my phone a few days back, overclocked my phone, and the phone is as smooth as ever. If you are ok with rooting the phone, I could guide you through the process (in case you brick your phone... lol)