Connolly returned to the Lightning after scoring five goals in six games as Canada won a bronze medal at the world juniors this week in Calgary and Edmonton.
The six-foot-two, 205-pound right-winger called the tournament a confidence booster.
"For me, it's just to continue the way I was playing," he said Saturday before the Lightning's game against the Montreal Canadiens. "Don't try to do too much.
"The last game I had (in the NHL) against New York I had a pretty good game. Just to build off the tournament I had and help the team win."
Connolly, drafted sixth overall by Tampa Bay in 2010, had four goals and four assists in 28 games before Bolts' GM Steve Yzerman freed him up join the Canadian junior team.
He had a rough start at the junior camp. He was asked by coaches to play a more physical and intense game, then went out and injured teammate Quinton Howden with a late hit in practice.
But he adjusted. As one of four players returning from the 2011 tournament, he was named an alternate captain and was one of Canada's top forwards in the tournament.
He called Canada's 6-5 loss to Russia in the semifinals a "crazy" game, as they fell behind 6-1 only to fall short by one goal after a furious third-period comeback attempt.
"It got out of hand there for a bit," said Connolly. "In the second intermission, we took a deep breath and tried to come out and give it our best effort.
"It was a character effort by all our guys. Our team was good. We had a lapse, and when it comes to elimination games, you can't take any time off. We'll all learn from that."
Coach Guy Boucher was glad to have him back.
"I thought he showed incredible character," Boucher said. "I was told that when it was 6-1, he was one of the first guys to stand up and say it wasn't over, and we know what happened after.
"He scored in almost every game he played, but what I liked was his drive and dedication to doing the details of a winner and that's what we're asking of him. Coming back, we don't want to change him or put pressure on him. Right now, he'll replace (J.T.) Wyman, because he's a right-hander and he's got speed like him."
Wyman and forward Adam Hall suffered upper body injuries in a 4-1 loss Thursday in Ottawa.
Forward Ryan Malone skated Saturday morning and it was to be a game-time decision whether he would face Montreal. If not, Boucher said he would likely use seven defencemen, including Brendan Mikkelson, who was acquired Friday from Calgary for forward Blair Jones.
"He's a big boy with speed," Boucher said of Mikkelson. "We wanted depth.
"We have too many injuries on defence. Not that we didn't like Blair Jones, but we needed help on defence."
The Bolts also called up hulking forward Pierre-Cedric Labrie to play his first NHL game in his home province.
"He's big and he hits hard," said Boucher.
The Canadiens were set to welcome back captain Brian Gionta after missing 11 games with an undisclosed injury.
"He seems to be on the mend," said Cunneyworth. "We're upping the ante as far as his workload, but we don't want to push too hard because there might be another setback."