LAS VEGAS — With Carmelo Anthony officially on board, Knicks rookie coach Derek Fisher guaranteed the Knicks will be a playoff team this season, and will eventually compete for a championship with Anthony as the “anchor.’’

The Knicks missed the playoffs during a miserable 37-45 campaign last season that nearly led Anthony out the door. Anthony had told confidants he didn’t want to ever experience a season like that again.

“My opinion is, based on our roster and who we’re going to become, we can compete for playing in the playoffs and playing for a championship in the Eastern Conference,’’ Fisher said Monday after the Knicks’ summer-league victory over Charlotte, in his first remarks since Anthony’s signing became official. “When that happens, putting dates on it, that’s not my job.’’

As constituted, the Knicks’ starting five may be Samuel Dalembert at center, either Amar’e Stoudemire or Andrea Bargnani at power forward, Anthony at small forward and J.R. Smith and Jose Calderon in the backcourt. Knicks president Phil Jackson may be viewing Stoudemire as a backup, and has told confidants he thinks Bargnani will have a big season in his contract year.

“I believe in our guys,’’ Fisher said. “Even if nothing else changes, we’re good enough to be a playoff team in the Eastern Conference, but we have to go out and prove it.’’

Fisher’s theme since getting hired last month was that basketball experts are underrating the Knicks’ talent.

“A lot of people feel everybody around Carmelo needs to be different,’’ Fisher said. “I don’t necessarily agree with the mind-set. We have some very good basketball players on our team.’’

Fisher has not spoken to Anthony since Sunday’s official announcement, but in their two meetings, the rookie coach has impressed upon Anthony that this season the offense won’t be all about him, as it was under Mike Woodson.

“I haven’t gotten to that point analyzing his individual game in terms of strengths and weaknesses,’’ Fisher said. “What I most thought about it [was] how much easier the game will be for him. We won’t just give him the ball and say, ‘Save the day.’ We’ll utilize guys around him to be successful, build trust, build chemistry, build a fun way to play for guys, and that will make our defense better.

“That’s what he wants. … He wants to be in an environment where everybody is effective. He wants a balanced basketball team.’’

Jackson has said the team still needs to add another rebounder and perhaps a another backup small forward in case rookie Cleanthony Early isn’t ready. Jackson could offer the $3.27 mini mid-level exception, but doesn’t want to dole out a long-term deal to cut into cap space in 2015 and 2016.

Fisher said he wants to build a strong relationship with Anthony.

“Whether player to player or coach to player, it’s about the relationship,’’ Fisher said. “I’m not nervous about building the type of relationship with Carmelo we both need for us to be successful. We’re human beings and grown men. We’ll talk and work together. I’m not nervous about being myself.

Fisher and Anthony weren’t friends when Fisher was still a player.

“I think there’s a great deal of respect that’s gone both ways,’ Fisher said. “Hopefully that will help us build a mutual respectful relationship. It’s a great opportunity not just for me, but for Carmelo. We spoke in person twice about what a coach could provide. He’s comfortable with that part. The toughest part for him was: Will our roster be competitive enough to win?’’