”“We had a good chemistry going forward and there is no question that our goal for next year is to make the playoffs and I think we’re all on the same page there. We all want to be there,” Wizards President Ernie Grunfeld said. (Jonathan Newton/WASHINGTON POST)

After missing the postseason for the fifth consecutive season, Washington Wizards team President Ernie Grunfeld said Tuesday he believes the team isn’t too far away from playing meaningful games in April, and possibly May, once again.

Betrayed by poor health this season, the Wizards stumbled to a horrific 4-28 start, but they ended the season going 25-25, with injuries again contributing to the team losing its last six games. Grunfeld believes that unlike prior lottery-bound teams, the Wizards have the young building blocks (John Wall and Bradley Beal), stabilizing veterans (Nene, Emeka Okafor and Trevor Ariza) and a defensive mind-set that should position the franchise for success next season.

“I think now we have a foundation,” Grunfeld said during a 30-minute news conference on Tuesday at Verizon Center. “We had a good chemistry going forward and there is no question that our goal for next year is to make the playoffs and I think we’re all on the same page there. We all want to be there.”

Wall has been the centerpiece of the Wizards’ rebuilding efforts since being drafted first overall in 2010 and is eligible to negotiate a contract extension beginning July 1. If a deal isn’t struck before the start of next season, Wall would become a restricted free agent in 2014. Wall averaged a career-high 18.5 points in his third season and has already expressed a desire to receive a maximum contract worth roughly $78 million over five years. While not discussing specifics, Grunfeld expressed a desire to get something done.

“I think John had a very good year, and he showed that he makes a difference on the team,” Grunfeld said. “Obviously, we’ve said all along that we’re building this team around John and with John. We want to have him here long term.”

Wall missed the first 33 games of the season with a stress injury in his left knee, which contributed to the team’s early struggles and provided the theme for a season of injury woes. Beal missed 26 games because of problems with his back, right wrist and right leg. Nene missed 21 because of plantar fasciitis and several other ailments that came as the result of compensation.

Together, the trio combined to appear in just 22 games and make eight starts together. The Wizards only had four players appear in at least 58 games.

“But I think that the number one thing is that we need to get our players’ health right. We have to rest up this summer, get our health right, and come back next year with all our players,” Grunfeld said. “When you don’t have all your pieces together, you’re asking different players to play different roles, and I think that was the case in the first part of the season. It’s an awkward situation at times for some of the players, but I think our players were very professional about it. They never complained about it, and when you get off to the tough start like we got off to, they could’ve quit. They could’ve just laid down, and they didn’t.”

The Wizards have the eighth-best odds (3.5 percent) of winning the May 21 NBA draft lottery. Wall, Webster and Coach Randy Wittman all pushed for the team to look toward other avenues other than the draft to improve to the team, but Grunfeld wasn’t ready to dismiss the pick.

“We can get an old player any time, but if the older player doesn’t help you on the court, that’s not the kind of situation we want to get into,” Grunfeld said.

Grunfeld praised Wittman for the role he played in guiding the Wizards through a difficult storm through the first few months and for creating a defensive scheme that allowed the franchise to finish in the top 10 in scoring, opponents’ field goal percentage and opponent three-point percentage for the first time in 26 years.

He kept the ship afloat. Kept the guys motivated. Kept them competitive on a nightly basis,” Grunfeld said. “Randy did a very nice job of putting the defensive concepts in there. . . . I think it’s been shown that the teams that have success, longer-term success and have success in the playoffs, are good defensive teams.”

The additions of Okafor, Ariza and Webster helped make the Wizards a slightly more competitive team than previous seasons, but younger forwards Jan Vesely, Kevin Seraphin, Trevor Booker and Chris Singleton — players chosen in the past three drafts – regressed with limited opportunities. Vesely plans to play for the Czech Republic national team this summer in Eurobasket, while Seraphin is unlikely to play for the French national team after participating the past two offseasons, including the 2012 Olympics.

“I think this is a big summer for all of them. They all need to improve, they all need to work hard,” Grunfeld said. “They're all under contract. So it’s realistic to see that they will be back. They'll tell us what to do by how much improvement they've made.”