The Chiefs fell to 2-1 with Sunday's 20-17 defeat to the previously winless Indianapolis Colts.
Only three times in Mahomes' career have the Chiefs scored fewer than 17 points in a regular season game.
The superstar quarterback completed only 20 of his 35 pass attempts for 262 yards and a single touchdown, also throwing an interception on the team's final drive as they sought to force overtime.
After scoring TDs on their first two visits to the red zone, the Chiefs returned only three points from their final two, with Matt Ammendola's fourth-quarter field-goal miss proving costly.
"I don't expect any growing pains," he said. "Obviously we have new players and you don't know everybody's going to respond to tough situations.
"We've got to gel all together. It starts with me. There were certain throws I was putting on guys' back hips instead of in front of him. There were certain situations where we were just barely off of it.
"Whenever you're playing a tough game like that, you have to execute at a higher level and we have to learn from it.
"Our schedule gets no easier. We have a hard game Sunday [against] Tampa next week with a great defense, so we have to get better quickly.
"And if we don't, we don't want these [losses] to start piling up. We want to make sure we get back on that winning train."
For the season, only the Detroit Lions (11) have scored more red zone TDs than the Chiefs (nine from 13 RZ drives), who rank eighth in red zone TD efficiency.
Last year, the Chiefs were 14th in efficiency, scoring 41 touchdowns from 68 red zone drives.