define "plastic". If it's a normal plastic container or tube that shouldn't be a problem.
In general Trizol is not likely to bt the problem or source of contamination for your samples. It is more likely that there was cross-contamination of your samples during a step of the extraction protocol or the samples were not properly stored.
In any case, try using fresh samples with new reagents and the same Trizol. If the problem persists, it is either the samples or the Trizol, although I would suspect the samples to be the culprit in this case.