Lewis Hamilton says he wants a "fair fight" with Mercedes team-mate Nico Rosberg for the title this season.Rosberg beat Hamilton to win in Monaco following a controversial qualifying incident that sealed the German's pole.
"This weekend went in a direction I wasn't expecting. I'm aware of it now. I'll make sure I'm aware in the future," Hamilton said.
Lauda said Rosberg, who was cleared of any wrongdoing following an investigation by race stewards, had denied this to Hamilton on Saturday.
He repeated that denial in a BBC television interview after the race on Sunday.
Rosberg's position was backed by Mercedes bosses including Lauda, the team's non-executive chairman and a three-time Formula 1 world champion.
Asked to confirm he believed Rosberg had done it deliberately, Hamilton said: "Look, man. The weekend's done and dusted. We've got a one-two for the team. Let's just focus on moving forward. I plan to be stronger in the next race."
He added: "We've sat down and cleared whatever air was needed to be cleared. We've been through the data and seen what needed to be seen. I wish you guys could see it. Otherwise, we're good.
"It was a difficult weekend but what doesn't break you will make you stronger. I can only get stronger for this weekend, I think."
Despite the tense atmosphere at the team, Hamilton said he believed he and Rosberg would be able to race against each other for the rest of the year without major incident.
"I think so," he said. "I think it is running successfully. It's never going to be perfect because we're fierce competitors, so you can never expect us to be best friends and compete as fiercely as we do. But we will remain respectful I think. Or I will try to remain respectful."
When he was told Lauda had said he expected them to have a crash together at some point, Hamilton said: "Niki keeps saying that but I think generally we have done quite a good job up until now.
"It was as close as it could ever really be in Bahrain and we didn't crash and so I don't think that's going to be the case."
The result in Monaco put Rosberg back into the championship lead with a four-point advantage over Hamilton.
It was the first time the German had beaten Hamilton on track in a race this season. His only previous victory came in Australia at the start of the season, when Hamilton retired with an engine problem. Hamilton won in Malaysia, Bahrain, China and Spain.
"The team is the priority and that's what we have to keep in front. That's what I kept my priority, the team. We want to get the points for the team. I didn't do anything silly, just looked after the car."
Rosberg said: "It's fine. We've had discussions and the benefit we have is that we've known each other for so long. We always sit down and discuss it and then move on and that's what we're doing this weekend also."