Johnson has been one of the league's top receiving backs in his first three seasons, but he has seen fewer opportunities during Cleveland's 2-2-1 start.
Carlos Hyde has been the bulk of the work for the Browns out of backfield. Signed as a free agent in the offseason, Hyde has rushed for 348 yards and five touchdowns. Rookie Nick Chubb also is in the mix, although he has received fewer touches than Johnson.
"He told me to just be more positive," Johnson said Thursday. "Just focus on all the good. It's not all bad. It's not all good. You're going to have some days when you're not feeling so well. Just find a way to get through it.
"He's very positive, he's a very good dude. It's his beliefs. It's what he believes in and I got a glimpse of that today just talking to him. Regardless, he's still our captain."
The fourth-year back acknowledged he has "a more positive practice" after Taylor's pep talk on Thursday and is trying not to let the frustration build.
Johnson has only 10 catches through five games, including two or fewer on four occasions. He rushed for a season-high 35 yards on five carries in last weekend's 12-9 win over Baltimore.
The fourth-year running back had 23 receptions through five games last season on his way to establishing a career high with 74 catches. He also rushed for a career-best four touchdowns in 2017.
"I don't think these games have to be as hard as they are," Johnson said. "I think I can help this team win given more opportunities."
Johnson amassed 188 receptions in his first three seasons and could be in line for more work. Browns coach Hue Jackson told Cleveland.com that an injury to wideout Rashard Higgins could provide more opportunities for Johnson.
"Duke's skillset allows us to do a lot of different things with him," Jackson said. "We split him out a little bit this past week, and I'm sure we will do other things with him as we go. Duke is very talented. Obviously, when he has the ball in his hands, good things happen."
Johnson and the Browns will host the Los Angeles Chargers on Sunday.