Actually the English
t is not always aspirated. For example, think about words like "light" or "stick" and compare them to, say "toy" and "potato". They are pronounced [laɪt], [stɪk], [tʰɔɪ] and [pəˈtʰeɪtʰəʊ] respectively. The latter two words have aspirated
t's in them, the former two don't (because the
t is at the end of the syllable in "light", and after
s in "stick"). When speaking Finnish, you should try to shed these rules from your mind and pronounce all
t's like in "light" or "stick"
Naturally everyone would understand you even if you aspirate your
t's, but it would sound foreign. Also, the same rule applies for
k and
p which are never aspirated either.