The Penguins (27-13-2) have won three straight games and are 9-2-1 in their past 12. They are third in the eight-team MassMutual East Division, two points behind the Washington Capitals and New York Islanders.
"Coming here and joining this team, the run they're on right now and the position that we're in, it's exciting," Carter said. "I can't wait to get back to the playoffs and make a run at it. Hopefully, we can get the job done."
Pittsburgh has been without forwards Evgeni Malkin (lower body), Kasperi Kapanen (lower body) and Brandon Tanev (upper body), each of whom is out week to week.
Hextall said he believes Malkin will be back before the Penguins are scheduled to end the regular season at the Buffalo Sabres on May 8. The center was injured during a game against the Boston Bruins on March 16. He has scored 24 points (eight goals, 16 assists) in 29 games this season.
The GM said Kapanen is expected to be out another 10-14 days after being injured during a game against the Sabres on March 24. Kapanen has scored 21 points (seven goals, 14 assists) in 30 games.
Hextall said Tanev's injury is tough to judge and that he doesn't believe he'll be back before the playoffs. He was injured during a game against the Bruins on April 3. Tanev has scored 16 points (seven goals, nine assists) in 32 games.
Center Frederick Gaudreau also is out week to week after sustaining a lower-body injury during a 5-2 win against the New Jersey Devils on Sunday.
"We've just kept winning games," Hextall said. "Guys stepping up. Colton Sceviour last night (two goals against the Devils). Gaudreau. You could go on about guys that have stepped up. Obviously, you've got [Sidney Crosby] and [Bryan Rust], and Jake [Guentzel] and Jared McCann's done a real good job. But it's some of the role players that have really stepped up for us. Again, it proves that we have quite a bit of depth here. We felt like adding one more forward would really solidify our group. I like our group right now, and when we get healthy, hopefully we'll stay healthy. Really like our group and we'd like to have some playoff success."
Carter's versatility and ability to play center or the wing is one of the things that made him attractive to the Penguins, especially with so many injured forwards.
"We're obviously thrilled to add Jeff to our group here," Penguins coach Mike Sullivan said. "He's a real good player. He's a proven player. He's a Stanley Cup champion. I think he can play the type of game that we're trying to play here in Pittsburgh. He can really skate. He has a great shot. He has versatility to his game. He can play center. He can play the wing position. We really think he's going to add to this group in such a positive way. We're thrilled to have him. I know he's excited to be part of our group and we think he's going to make us a better hockey team."
Carter said he doesn't have a preference as to which position he plays for Pittsburgh.
"I can play both. I'm comfortable with both," he said. "I was mainly a center up until the time I came to L.A. Then was on the wing, went back and now I'm back on the wing. So I'm totally comfortable with both. I haven't had any discussions yet with the coaching staff on my role and where it all fits. But I'm sure we'll find out more tomorrow at practice."
The Kings (16-19-6) are seventh in the eight-team Honda West Division, six points behind the fourth-place St. Louis Blues, and have won three of their past 11 games.
The top four teams in each of the four divisions qualify for the playoffs.
"We believe this team is capable of making some noise, especially adding Jeff," Pittsburgh president of hockey operations Brian Burke told Sportsnet. "We had chances to move some guys out and refused to do so. These guys have worked so hard. We've got good chemistry and we'll start getting healthy here pretty soon."
NHL.com independent correspondent Wes Crosby contributed to this report
