Brady dispelled that notion on Thursday in an interview on WEEI's Dennis and Callahan program.
"Those aren't my demands. I want us to field as competitive a team as we possibly can and I have all the trust in the world that Mr. Kraft and Jonathan [Kraft] and coach Belichick do that. I'm not general manager, I can't say 'I do this, you do this,'" Brady said. "I think we are going to field a competitive team."
However, when Welker left in March to join the Broncos and the Patriots signed Danny Amendola to replace him at slot receiver, comparisons between the two became inevitable. Brady thinks those comparisons are unfair.
"They are similar positions, they're about the same height, they've both got very good ability. Wes was so productive for so long, I think it's unfair to compare anyone to Wes and what he was able to accomplish in his time here," Brady said. "Danny has been fun to work with. He's come in with an open mind and an understanding of the way we need to play."
Brady also said he was not surprised to find out Welker would be leaving the Patriots. After six seasons in New England, Welker signed a two-year deal to join the Broncos in March.
"I don't think anything surprises me anymore in the NFL," Brady said. "I've been around long enough to see different things happen at different times with the greatest players of all, whether that's Wes, or Randy Moss being traded from the Raiders, or Brett Favre playing for the Jets and Vikings. That's what happens."
Brady remains close friends with Welker, but wouldn't say if he was angry the Patriots let Welker leave as a free agent.
"Of course I have feelings, but those feelings are very personal to me. I used to get caught up in anger and frustration and disappointment, but I don't make the decisions. These things aren't up to me," Brady said.
Brady has spent his offseason working with throwing coach Tom House and has been seen at several high-profile events, including the Kentucky Derby. A now-famous video shows Brady and friends gleefully celebrating a victory by Orb. He explained why he was so pleased with the race's outcome.
"We went down with a friend of ours who was an owner of the horse, so we kind of had a rooting interest, and we had a rooting interest for several months. So it's kind of like we were very much a fan, and I haven't had that experience in a very long time where you're just very happy that someone else won. I was, I would say, overjoyed," Brady said.