I think that the problem with an FR-4 board can be:
1. As FR4 is a relatively cheaper board, the fabrication tolerances are quite high. So it is hard to be sure about the exact value of relative dielectric constant. However, in case there are any differences in simulated and measured results arising due to FR4 board, you should be able to trace them back by parametric simulation in the software.
2. FR4 is not exactly a low-loss board, hence not an ideal choice for an antenna. There are better boards which provide lower losses , but then they cost you more.
So if you're looking to validate a concept for a study, use FR4. There might be some errors arising due to the board, which you can explain by retro-simulation. If you're looking to put an antenna in an application, look for a better substrate.
Actually when I am simulating the structure in HFSS it is showing good result. But I am in doubt if the measurement result will vary than that of the simulation one.
If there is a shift in the resonant frequency of the antenna, you can explain it by dielectric constant (or a fabrice correctly puts, effect dielectric const.).
If the realized gain of the antenna is lower than that observed in simulation, it may be due to a variety of factors, amongst them losses in dielectric. Assuming that you take care to measure accurately enough, then lower gain can be explained by dielectric loss (tand).
As an alternative, you can try to simulate with other substrates such as Rogers Duroid or Arlon CuClad wovenglass/PTFE. As I said, if this is just to validate a design, use FR4 and try to resimulate in HFSS the difference in the results. However, if you're looking for a practical application where performance of the device is essential, then look towards buying costlier substrates.
FR4 is a lossy substrate and exhibits poor performance with the increase in frequency and certainly not a good choice at higher frequencies. Although, S11 and gain can be optimized, difficult to achieve high efficiency. However, for research purpose, as it is cheap and easily available, can be used for prototype testing presenting new results/ideas.