Liverpool beat Macedonia's Rabotnicki 2-0 for a 4-0 aggregate success in a Europa League third qualifying round tie on Thursday, Hodgson's first home match in charge since replacing Rafa Benitez last month.
Hodgson said continued takeover speculation had not affected his preparations, but any dealings in the transfer market might prove difficult if an ownership battle raged.
The 18-times English champions were put up for sale by American owners Tom Hicks and George Gillett in April and on Thursday there were a number of claims and counter-claims about the club's new owners.
"I was totally concentrated on the match, that took my total focus. As and when a takeover happens I am sure I will be the first to know," Hodgson told reporters.
"But regarding any takeover, I think the danger would be in a late takeover that money would become available - but we would not have had a chance to research the players during the transfer window.
"We are doing our research now targeting players the club is capable and able to buy. If one day an enormous amount of money is made avaliable as it was to Manchester City and to Chelsea, so be it, that would be nice.
"But we would still have to do a lot of research and background work before we start to splash that money around. It's not a question of how much a player costs, it's how good he is."
Hodgson was full of praise for his team - and also the crowd, which totalled 31,202 fans.
"We have had a good performance and a win and I am as happy as the players and the fans are. I must say I am surprised by the size of the crowd for the match after we won 2-0 away from home against an unfancied opponent and to still attract a crowd of over 30,000 people is fantastic.
"It is also great for me that Joe Cole had such a great debut in front of that crowd to show them they are going to get a lot of joy from him this season."
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