The Dens Park side suffered a seventh league game in a row without a win this term when they lost narrowly to champions Rangers after Joe Aribo's first-half goal proved decisive.
However, McGowan insists Dundee have a strong squad and are playing far better than their results suggest.
He said: "If we keep playing the way we're playing… I've been here for seven years and I've been involved in hard times. But I'm not down just now.
"The boys are not down because we know it will come and the goals will start to come.
"It's been tough but you can see the fans are sticking with us. You can't ask for more. We're creating big chances and not taking them, and being sucker punched.
"It was a great goal by Rangers but we didn't take our chances. We have a proper team in there and it's the best squad I've been involved with."
The game's most pivotal moment came in the 58th minute when Dundee were awarded a penalty after Jon McLaughlin fouled Paul McMullan in the box. The Rangers goalkeeper was shown only a yellow card when the hosts felt he should have been sent off, and he subsequently saved Jason Cummings' spot-kick.
McGowan said: "I think he should have been (sent off) because wee Paul was going to tap it in. He's knocked it by him by about five yards. That goes against us as well and he saves the penalty.
"I feel for the boys because we put so much into the game. We need to keep our heads up and the results will turn."
The game marked Rangers captain James Tavernier's 300th appearance for the club since he arrived in 2015 when they were in the Championship.
He told Rangers TV: "300 games is a lot of games. It feels like they've come fast. It's about the overall team progression we've had since I've been here. We're reaching new heights and always demanding and wanting better from each other.
"It's been some journey. It's been a roller-coaster. We've had last season where we were successful in the league but we want to improve on that and try to get into the Champions League next season and be better in the domestic cups.
"We're always hungry for more. It's been a great journey but there's loads more to go. I can't wait to see what the future brings."