It turns out that I use this word far more often than I thought. When you think about it though it's not exactly clear what 'impressed' means in English. If you're impressed by a work of art does it follow that that work of art makes you happy? Not necessarily. I suppose 'impressed' is a less intense form of 'amazed'. Well, the Romans had the word 'mirum' but out of three books of synonyms that I have, Ramshorn (1860), Doderlein and Horae Latinae, none of them have a list of synonyms for 'mirum'
I just tried 'admirari' and Ramshorn does analyze the difference between 'mirari', 'admirari', 'suspicere', 'demirari' and 'stupere'. All of them to me seem to be more intense than 'impressed' but 'suspicere' seems like it might work, so I'm going to go with the participle of 'suspicere' which is 'suspicatus'. Also at https://latinitium.com/latin-dictionaries/?t=do534 they analyze the difference between:
vereri; revereri; venerari; colere; observare; adorare; admirari; suspicere; verecundia; reverentia; veneratio; cultus; precatio
Also, I looked up all the words related to 'premo' and it appears that the Romans did not adopt the verb 'press' to figuratively mean 'impressed'.