Presence of spectral curvature due to synchrotron self-absorption (SSA) of extragalactic radio sources may break down the spectral smoothness feature-the premise that bright radio foreground can be successfully removed in the 21cm experiments of searching for the epoch of reionization (EOR).We present a quantitative estimate of the effect on the measurement of the angular power spectrum of the low-frequency sky,incorporating a phenomenological model,characterized by the fraction of radio sources with turnover frequencies in 100-1000MHz range and a broken power law for the spectral transition around turnover frequencies nu_m,into the simulated radio sources over a small sky area of 10x10 deg^2.We compare statistically the changes in their residual maps with/without inclusion of the SSA after the bright sources of S_150MHz>=100mJy are excised and the best-fitted polynomials in frequency domain on each pixel are further subtracted.It has been shown that the effect of SSA on the detection of EOR depends sensitively on the spectral profiles of radio sources around the turnover frequencies: A hard transition model described by the broken power law with the turnover of spectral index at nu_m would leave pronounced imprints on the residual background and cause serious confusion with the EOR signal.However,the spectral signatures on the angular power spectrum of extragalactic foreground generated by a soft transition model,in which the rise and fall power laws of spectral distribution around nu_m are connected through a smooth transition spanning >=200 MHz in characteristic width,can be fitted and consequently subtracted by employment of polynomials to an acceptable degree(delta T<1mK).As this latter scenario seems to be favored by both theoretical expectation and radio spectral observations,we conclude that the influence of SSA on the 21cm experiments is probably very minor.