Can a small monitor influence video game performance?

Hi! I recently bought a PC (AsRock H55M-GE PCI Express 2.0, Intel Core i3-540 3.06 GHz, 4 GB DDR3, Sapphire ATI 5450HD 1GB GDDR3, 500 GB HDD). I have Fujitsu Siemens Monitor which is 15 inch wide. I am using Windows 7 Ultimate 32 bit and I have some problems in games like NFS Most Wanted or GTA San Andreas. It doesn't run smooth. These games aren't new games like Crysis or Test Drive Unlimited 2. The guy from which I bought this PC said that I may experience some issues because of my small monitor. Is this true and what can I do to solve this problem. Thanks