Stuart Armstrong added a second after the break as champions claimed a 2-1 win which moves them one win away from securing their sixth straight title.
But Simunovic says his strike was all the more special after being forced to battle back into Rodgers’ line-up.
He said: “I have worked hard in the last month. I didn’t play much but my work paid off.
“I showed that against Dundee. It’s part of football. You never know what happens tomorrow, so you use every day like it’s the last of your life. That was my thinking every day last month.”
Victory over Hearts at Tynecastle next Sunday – or an Aberdeen defeat by Dundee on Friday night – will seal Rodgers’ first Ladbrokes Premiership title since taking over last summer.
But Simunovic insists the Parkhead side will not get carried away just yet.
“The title is close and it’s very exciting,” he said. “We’re excited about the next game at Hearts and we want to finish it off in the right way.
“The consistency we have shown has been fantastic. It’s not easy to continue winning every game but we prepare for every game the right way. We’ve done that all season and we just want to continue that.
“It was good to get the goal on Sunday. I always believe I can score but the most important thing is the team. It didn’t matter who got it.
“I felt very good and, in the end, we finished in the right way. I am happy with that.
“It was a scrambled goal but the most important thing was that we scored. It doesn’t matter who scored.
“We put on the pressure in the last minute of the half and that’s always the best time to score.
“It is always hard to play at Dens Park. It was a tough game but we had a clear aim for what we were going to do and we won. It was most important we got the three points.
“We showed a good performance and did very well.”
Simunovic has not been included in Croatia’s squad for this month’s World Cup qualifier with Ukraine, but Rodgers has 13 men away on international duty, including six who are members of Gordon Strachan’s Scotland squad.
The Parkhead boss wants them to forget about club duties until they return.
“I always say to the players when they go away to think of their countries, don’t think of Celtic,” said Rodgers.
“They need to look after themselves, make sure they do the right things well and play as hard as they do here.
“Hopefully they all do well and return healthy.”