The genomes are from same species. Is it true that, in phylogenetic tree constructed from amino-acid based MSA (multiple sequence alignment) some information are lost, so for phylogenetic reconstruction of closely related sequences nucleotide based MSA should be used?
For a species complex nucleotide phylogenies all the way.
The reason is neutral mutation, which is not observed at the amino acid level because these mutations are part of the degenerate code which don't induce amino acid substitutions. Such mutations are commonly referred to as the third codon wobble, although occasionally the first codon can mutate and not produce a change in amino acid.
Neutral otherwise known as synonymous mutations occur at a much higher rate than mutations that cause a substitution of an amino acid. This is the reason why you were told information is lost at the amino acid level because you're losing neutral mutations.
There are circumstances when the amino acid phylogenies are preferred to nucleoside trees, but these are bit pretty specialised areas.