Assistant general manager John Ricco also attended the meeting before Monday night's game against the Braves.
The Mets have lost five straight to fall to last place in the NL East, but Manuel said "I have not been concerned about my status."
"We have shown that we can play," Manuel said. "We have to get back to that."
Manuel said the meeting was "a good baseball meeting" to discuss "our plan going forward."
Manuel was in good humor when he briefly left the meeting and told reporters "I got a uniform on, brother." A smiling Manuel then returned to the meeting.
Wilpon said he wanted the meeting following four straight losses at Florida.
"I didn't come here to fire anybody, guys. Sorry," Wilpon said.
"We played four poor games in Florida and I felt like it was time to come down to meet with the staff."
Wilpon said he wanted "to get a sense of where they think we are at and what can be done to get the team moving forward again."
Wilpon said similar meetings are held regularly in New York without causing a stir.
When asked if Manuel's job is in jeopardy, Wilpon said "If I was going to make a change that quick, I would have made it last year."
The Mets are 4-11 in May following a 14-9 record in April. They began the two-game series against the Braves with big questions in their rotation.
Left-hander Jonathon Niese is in New York after suffering a mild strain of his right hamstring on Sunday. Another starter, Oliver Perez, was sent to the bullpen on Saturday.
Manuel said he has not picked a starter for Wednesday's game at Washington.
The Mets appear close to promoting right-hander R.A. Dickey from Triple-A Buffalo. Dickey's name was over a locker in the Mets' clubhouse early Monday but was later removed because no transaction has been announced.
Dickey opened the 2009 season with Minnesota, where 34 of his 35 appearances came in relief. He was 1-1 with a 4.62 ERA. He was 5-8 with a 5.21 ERA with Seattle in 2008 and previously pitched for the Texas Rangers in parts of five seasons.
Niese hurt his right hamstring for the second time in a year. He missed the final two months of the 2009 season after surgery on Aug. 6 to repair a torn hamstring tendon.
Niese hurt the hamstring on Sunday when he fielded a bunt in the third inning and planted awkwardly before making a wild throw that allowed a run to score. He made one more pitch before leaving the game. He was examined in New York on Monday.
New York's starting pitchers were winless in 15 games in May entering Monday night's game against the Braves.
AP freelance writer Amy Jinkner-Lloyd in Atlanta contributed to this report.
(This version CORRECTS SUBS 16th graf to correct to R.A. sted J.A. Dickey)