Recent attacks and death threats directed at Celtic manager Neil Lennon have overshadowed a tense Scottish Premier League season and McGowan, who spent part of the campaign on loan with Partick Thistle, says it does not look good for Scottish football.
McGowan played in the match when a fan charged the pitch and attacked Lennon at Tynecastle Stadium last week and was disappointed and ashamed by the events which unfolded.
"It doesn't reflect well. Scottish football will now be broadcast in Australia for that incident - not for Celtic winning or a good game, which I thought it was," he told the Daily Express.
"I've certainly never seen anything like that back home. We're too laid back to get that worked up about stuff. But it's a one-off incident that isn't good for Hearts.
"It doesn't reflect well on the club and we're disappointed in the individual."
He added: "The game against Celtic was frustrating. There was a good atmosphere at the start but then it turned sour.
"I missed what happened with the crowd but it's not really football, is it? You don't want to see that at any ground, anywhere.
"It's all everyone's going to be talking about. As footballers we don't want to be talking about these things. We'd rather be talking about stuff that happens on the pitch.
"There's no place for it. It shows the passion but there has been a line that has been crossed this season."