Hajnal scored his side's only goal in the 3-1 defeat but admitted that his goal mattered little as the damage has already been done.
"There was no more in it for us this evening because we conceded the two goals so early on," he told the club's official website.
"We had high hopes for this one but had to pick ourselves up early on. The goal in the second half didn't really help then – we just need some wins right now."
Stuttgart return to league action on Sunday against Eintracht Frankfurt.