The Tigers prevailed in a thriller at the MCG and broke a nine-game losing streak against the Blues on Thursday night, but not without some nervous moments.
Hardwick said he had faith his players would hold on as a 42-point lead was whittled away, as the rampaging Blues kicked eight of the last 10 goals to cut the final margin to just five points.
It was the Tigers' first win in their season opener since Hardwick took over for the 2010 season and he didn't want to see it go to waste.
"You've got to take advantage of it," Hardwick said on Thursday night.
"There's no doubt early wins are important to get your season up and going, we spoke about that.
"They can enjoy the win tonight, but we've got St Kilda in seven days' time as of tomorrow. We've certainly got an opportunity to get some wins."
Hardwick said he was disappointed "to a degree" that Richmond had let Carlton back into the game, with his team "unable to control the ball at any stage" in the frantic final quarter.
"There's no doubt I reckon there were stages where we controlled the game and probably should have been a lot further ahead on the scoreboard," he said.
"Carlton are a very good side and they've got an outstanding list. They just don't give up and Mick Malthouse sides don't - we just had to control the ball.
“Our guys knew what to do, but we just couldn't get the run in our players. We had a number of players cramping, as did Carlton."
Hardwick praised key forward Jack Riewoldt, who finished with 0.4 but still played "one of the best games he's played in 12 months".
"He played a pretty significant role tonight, Jack, by dragging a couple of their defenders up the ground," Hardwick said.
"I thought he was outstanding. It allowed Ty (Vickery) and Luke McGuane to get down deep, which was great … he won a lot of crucial contests."
The coach was also pleased with midfielder Brett Deledio, who kicked two brilliant running goals from beyond 50m.
The vice-captain was one of the most influential players on the ground despite having a modest 17 disposals.
"I thought he was a big game player; when his touches were there they counted," Hardwick said.
"Brett's come on enormously with his leadership. He wants to lead and it's showing in his footy now, which is really important."
Nathan Schmook is a reporter for AFL Media. Follow him on Twitter: @AFL_Nathan
