St Kilda announced on Thursday that Richardson would coach the club for the next three years.
Thomas said the Saints' last-minute search for a senior coach had created a "flow-on effect" that had disrupted the Power's 2014 preparations and would ultimately lead to the disadvantage of another club when Richardson was replaced.
"The unfortunate thing about this is that there's a flow-on effect; we're going to be affecting someone else's program," Thomas said.
"That's the situation that unfortunately the St Kilda footy club and their process has put us in … I don't know any way of avoiding it.
"We made that comment to the AFL today - the situation leaves us with no choice.
"We're going to be going to the best candidates, people who are willing to come to Port Adelaide."
Thomas said Richardson's replacement would be found "as soon as possible" and confirmed that a list of candidates had already been compiled.
But arguably the most pressing issue for the Power now is the intimate knowledge of the club's draft strategy Richardson takes to St Kilda.
Just a week from the NAB AFL Draft, both Richardson and the Saints' interim CEO Michael Nettlefold have offered Thomas and the Power their word that secret information wouldn't be divulged.
"The draft is a real issue. All that we could do is, I spoke to their CEO, I spoke to Alan, they gave me their word that there would be no sharing of information regarding Port Adelaide's list priorities," Thomas said.
"I can't do any better than that; you have to take these guys on face value and we will.
"I know them both well, they have given me their word in good faith, that's the best we can do."
While Thomas insisted the club had to "suck it up and get on with it", he said the timing of St Kilda's coach hunt was an issue he would be discussing at next week's CEOs' conference.
"We are a week away from [the] draft, we are well into our planning for 2014, the players arrive back next week and we're trying to now think about replacing a director of coaching," he said.
"We don't think that's good practice.
"What we've been talking about today with St Kilda is the lateness of the process and I think it's an industry issue that we'll probably discuss next week."