From the Wikipedia entry on statistical inference:
Inferential statistical analysis infers properties about a population: this includes testing hypotheses and deriving estimates. The population is assumed to be larger than the observed data set; in other words, the observed data is assumed to be sampled from a larger population.
From PSU online course:
Recall, a statistical inference aims at learning characteristics of the population from a sample; the population characteristics are parameters and sample characteristics are statistics.
If you are truly working with the population, you do not need to do ANOVA. You can compare the calculated means of different groups without any statistical tests because those calculated values are the population means.
It's worth thinking about what your population is. Maybe your data is just sample from a data-generating process (e.g. a snapshot in time) and you want to make inferences about the group means from that data-generating process.