Tate, the team's leading receiver in catches (44) and yards (517) this season, was dealt to Philadelphia for a 2019 third-round pick. The 30-year-old receiver is in the final year of his contract.
"For us, it's again the holistic picture of taking a look at what's best for us to do as a team and in those situations. They are not easy decisions, and they are certainly difficult decisions," Patricia said. "Again, for us, it's not about one player. It's about a team. It's about everybody. We have a lot of guys that are really good on this team that can produce, and honestly, for me, we have confidence in everybody on this team right now, that everybody can go out and do their job.
"I think we've seen through the course of multiple different examples of years in the NFL where these things happen and people move on and they keep going and they keep winning. So, is it difficult to win in this league? One hundred percent it is. Every single week is hard, so we're just going to have to work harder and keep going."
Patricia said he spoke to his players about the deal and stressed to them that they have to start preparing for the Vikings on Sunday and that he believes in the players Detroit has on its offense even without Tate.
"The biggest point for me to make sure everybody understands is that this also shows a lot of confidence in the people that are in that room," Patricia said. "There's great players in that room and there's a lot of them and there's a lot of guys that have opportunities to go out there and make plays and go out there and play at a high level, and we're all good with that from that standpoint."
The first-year Lions coach said Detroit would replace Tate with a multitude of players depending on the situation and the game. Likely candidates include receivers TJ Jones and Brandon Powell, tight end Michael Roberts and running back Theo Riddick.
"You never want to see somebody go, whether it's one day or four-and-a-half years, you build a rapport with the people around you," Jones said. "So any time someone leaves, it's a shock. It's something you go through. You want to comfort them but also give 'em space to adapt to their new team and all of htat. I think everyone is just supporting him but we all know the task at hand here."
The decision to deal Tate, though, appeared to come down to short-term gains versus long-term goals in the team's evaluation of whether to keep Tate.
"it's important for us, when we evaluate everything that we do as a franchise, I think there's certain value that we can get at times during the season that will help us long term and obviously have faith and confidence in the people that are on this team right now," Patricia said. "So we put all that into play and we're trying to make the best decision we can in that moment, and it's hard, very difficult when you're in that 'one game at a time' mindset and that's really where we are, from the standpoint of it's week to week for us and that's good, but there's also a big picture here that is good for those to keep an eye on as we move forward.
"That's something we always have to consider when we make all these decisions, whether it's during the season, during the offseason, free agency, draft, whatever it is, those are difficult decisions no matter when they come up."
Detroit signed linebacker Kelvin Sheppard to take Tate's vacant space on the roster. He's the fourth former Giants front-seven player to be brought in by Detroit this year, joining linebacker Devon Kennard, nose tackle Damon Harrison and defensive end Romeo Okwara.