Danny Lennon's side kicked-off the Scottish Premiership campaign by sliding to a 3-0 humbling at the Caledonian Stadium back in August.
While Inverness have since climbed to second spot in the table, it took Saints another seven games before they could finally secure their first victory.
The Paisley men now welcome Caley Thistle and their new boss John Hughes to St Mirren Park and Goodwin has promised the Highlanders will not have it so easy this time round.
He said: "We were very poor at the start of the season and we didn't get off to the start we wanted when we played Inverness on the first day.
"But we are a completely different team this time around. I imagine we will be much tougher opponents for Inverness now.
"We were not panicking in those early days but we were disappointed with how we started because we put in a lot of hard work during pre-season. We wanted to hit the ground running but ended up wasting the first six weeks of the season.
"I'm delighted to say we turned it around. The atmosphere in the dressing room is a lot brighter - it's night and day really. Winning games brings confidence and the boys are bubbly now.
"But we are under no illusions, we have a difficult run of games coming up. For us to keep the confidence up we need to keep winning games."
Hughes replaces former Caley Thistle boss Terry Butcher after the Englishman was lured to Hibernian.
But Goodwin believes Hughes - a former Easter Road manager himself - has the right credentials to keep Inverness soaring high in the top-flight.
"When I was at Celtic as a boy, John was there as a very vocal character within the dressing room," said the Irish midfielder.
"He was a leader on the pitch and having spoken to players who have played under him since, he has carried that into his management career. I know Kevin McBride who worked with Yogi at Falkirk and also spoke very highly of him.
"Yogi has been waiting very patiently to get back in at the top end and I'm sure he has jumped at the Inverness job when it came along.
"He's got a hard act to follow though. What Terry Butcher did up there is nothing short of a miracle when you think about the budget he had to work with. He did well bringing up some of the loan players from England that nobody really knew about.
"But I can understand Inverness' appointment of John. Terry and Maurice Malpass are such strong characters and they have replaced them like for like with John because he is very similar. He will want to get a similar reaction out of the players."