The Baker Mayfield era in Cleveland is not going to begin this week.
Taylor was 15-of-40 for 197 yards, one touchdown, one interception and a passer rating of 42.6. He was also sacked seven times.
"He's the quarterback," Jackson said Monday regarding Taylor. "His job is to get the offense to play the best they can play. It takes more than just him. It's the offensive unit as a whole that has to play better."
Mayfield, the first overall selection in the 2018 NFL Draft, did not get into Sunday's game and will not be the starter in the Browns' second game against the New Orleans Saints on Sunday.
Jackson did not absolve Taylor of all the blame.
Reminded of Taylor's 15-of-40 completion rate, Jackson said, "Not good enough, but it's not all on him. Does he have to do his job better? Yes."
Jackson noted that getting hit so many times did not help.
"When you get hit up a few times it becomes a little different," Jackson said. "He took one shot that was really, really tough."
Jackson also was critical of his team's running attack, which accumulated 177 yards on 38 attempts.
"I didn't like it," Jackson said. "Our quarterback was our leading rusher."
Excluding the sacks, Taylor rushed for 77 yards on eight attempts.
DE Emmanuel Ogbah might miss next week's game against the Saints and possibly more contests beyond that because of an ankle injury. Jackson said the third-year defender "may miss some time" with the injury. But, said Jackson, "I don't think it's the ankle sprain that lasts six weeks or whatever that is."
WR Josh Gordon started Sunday's game even though Jackson had said last week that Gordon would not start. Jackson said Monday it was a case of "miscommunication."
Jackson said Gordon was in because of a personnel grouping the Browns used to open the game. "He played on the first play, and that was a mistake," Jackson said. Gordon had one reception for 17 yards and a touchdown.
RB Carlos Hyde was the team's leading rusher among running backs on Sunday, gaining 62 yards on 22 carries, an average of 2.8 yards per carry.
RB Nick Chubb, a second-round draft pick this year, had three carries for 21 yards, including a run of 17 yards.
WR Jarvis Landry was the team's leading receiver with seven catches for 106 yards.