Speaking before a fan event Thursday night, Mularkey indicated reports saying otherwise were false.
"Don't believe everything you hear or read in the media," Mularkey said. "It's hard not to want a guy like that. We wouldn't have tried to trade for him if we didn't feel like we didn't want to have him here. There were a lot of things that went into this thing to try to get Tim to come here.
"In the long run, it did not work out. But if you do not want a player, you don't even get involved with it."
There were reports Jacksonville's front office and coaching staff didn't really want Tebow. Owner Shahid Khan certainly did, telling general manager Gene Smith to explore a trade for the polarizing quarterback.
The Jaguars offered a fourth-round draft pick for Tebow, but the former Florida star ended up going to the New York Jets for two picks.
So if the Jaguars really wanted Tebow, who grew up in Jacksonville, why not give up a third-round pick?
"That's confidential," he said. "The draft is how you build a football team and that's what we're going to continue to do. That's been the philosophy of this franchise. That's my philosophy. You've got to be very careful what you start doing with draft picks and we feel strongly about the draft."
The Jaguars have drafted three starters -- defensive tackle Terrance Knighton, cornerback Derek Cox and guard Will Rackley -- in the third round the past three years under Smith. They also chose defensive tackle D'Anthony Smith, who has yet to play a down in the regular season because of injuries.
Mularkey said internal talk about acquiring Tebow included him coming in as a backup QB. The coach declined to say whether the Jaguars intended to use Tebow mostly on special teams.
"Some of that's confidential to talk about, but we talked about all scenarios as far as the backup quarterback," Mularkey said. "He has some rare ability to do some things and all of that was discussed."
"I wanted to make sure they were updated with where things are and where they aren't, and that what we told them from the beginning had not changed," Mularkey said. "We wanted to reconfirm it. We hadn't been in contact with (Gabbert) for a number of weeks because of the way the new CBA is, but I just thought with the way things were going down it was important he heard from me and my belief in him and that why we brought him here had not changed."