The Maple Leafs (27-42-6) have lost seven in a row and host the Senators on Saturday.
Pirri, a 23-year-old Toronto native, has 20 goals in 41 games, including 11 in his past 13.
"It is really special," Pirri said. "I had a lot of friends and family here tonight, and for my first [NHL] game in here it was great. I played here as an elementary-school player in the city championships and this was my first time back. It was a lot of fun."
Toronto had the better scoring chances in the first period, but Florida took a 3-0 lead in the second.
"It wasn't the start we wanted, but in the second period we showed what we can do," Pirri said. "In the third period I think we took some time off and luckily [goalie Roberto Luongo] held us in the game. If we're going to get in (the playoffs) we're going to have to play a full 60 minutes every night."
"I don't think we had our legs at the start of the game, and I don't think our line (with center Aleksander Barkov and left wing Jonathan Huberdeau) played very well," Jagr said. "I was tired … emotionally tired. It is our job to score goals for this team. The coach has given us the opportunity to play together, and our line didn't do a good job in the first period. Then we got our legs back and we had two or three good chances."
The Panthers continue their five-game road trip with games against the Montreal Canadiens (Saturday), Senators (Sunday) and Bruins (Tuesday).
"I have been here 12 games, and in my opinion we could have won all 12 of those games," said Jagr, who is 7-4-1 with Florida. "We have big bodies and we can cycle and skate. If we play our game, we are a tough team to beat. It's up to us now."
The Panthers took a 2-0 lead when Huberdeau and defenseman Steven Kampfer scored 30 seconds apart.
Huberdeau scored his second goal in as many games, 13th of the season, at 4:23 on a high shot to the glove side of Toronto goalie Jonathan Bernier.
Kampfer's sharp-angle slap shot beat Bernier on the short side at 4:53.
Pirri made it 3-0 at 14:34 with a low wrist shot from the top of the left faceoff circle in the Toronto zone that beat Bernier through the five-hole.
The Maple Leafs replaced Bernier with backup James Reimer following the goal.
Pirri scored an empty-net goal with 1:36 remaining.
"First of all it was a great play by Morgan Rielly to take it into the zone and take it wide around the [defense]," said Carrick, who played his 14th NHL game. "I kind of went to the net with my stick on the ice and he found me for an open net. It was a great play by Morgan. …
"I kind of blanked out. After thinking about it now, it's kind of a dream come true. I was a little bit surprised the puck came out to me, and I was just happy to put it in."