The Premier League champions' have lost six of their opening 11 games and are 15th in the table as several of the club's leading players such as Eden Hazard and Diego Costa struggle to hit the form that helped Chelsea win the title last season.
There have even been suggestions that an increasingly rattled Mourinho has lost the support of the dressing room, but Lampard says that should never be the case.
"It's nonsense if it is happening," Lampard, Chelsea's record goalscorer and three-times Premier League winner, twice under Mourinho, told Sky Sports.
"I don't think players at the top level can down tools. The first responsibility is yourself, if you are downing tools, the only one that looks stupid is yourself."
"They're playing for Chelsea now and it is a huge club. They have to produce," he added.
Lampard, who left Chelsea for New York City FC, and spent last season on loan with Manchester City, believes Mourinho is still the man to lead Chelsea out of their current malaise.
"Stability is the ideal. Manchester United were the ideal with Sir Alex Ferguson and the same with the great Liverpool managers of the past, it's the ideal," he said.
"You want to see a manager stay, you want to see young players coming through, and that's the intriguing thing to see now, to see if Chelsea stick with him.
"He's got a four-year contract and he has got the best record as Chelsea manager. He is proven world class, and I think they should stick with him."
Lampard watched Chelsea's 3-1 home defeat by Liverpool last weekend, saying the players were off the pace.
"Jose Mourinho loves a high-intensity game, and I didn't see that," the 37-year-old said. "I watched Chelsea press (against Liverpool), and it was broken. When you are a couple of seconds late, the opponents can play out.
"I don't think I'm being over-critical, I know the boys, but some people are leaders and vocal in the dressing room. We all know Chelsea have had that spine for quite a few years, but you look around now, and you think do they (still)?"
(Reporting by Martyn Herman. Editing by Patrick Johnston)
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