The two men looked to be heading in different directions in January when Poyet finally managed to prise Scotland international Bridcutt out of the grasp of former club Brighton as Stoke stepped up their interest in Cattermole.
However, while the Black Cats got their man, the Potters did not, and that left them fighting for the one of the key positions in the Uruguayan's team, sitting in front of the back four.
Bridcutt, 24, has impressed in recent weeks, but he was ineligible to play in last weekend's Capital One Cup final defeat by Manchester City, and the quality of 25-year-old Cattermole's performance has significantly improved his chances of edging the new boy out in the longer term.
Poyet, who has made no secret of his admiration for his recent acquisition over the years he has worked with him, said: "It's going to be difficult for Liam, it's as simple as that.
"Sometimes you try to explain to players and they get it; sometimes they think it's just words. But when you are on the pitch and you have the chance to perform, if you perform, if you [the team] play in a week's time, you are going to be there.
"When [Vito] Mannone was Man of the Match, the week after, he played; when Wes Brown was Man of there Match, the next week, he played.
"It's not like you are going to change it for the sake of changing. It's fair competition and then the one who wins is the team because you get the best performance from the player."
Cattermole, who was discarded by former manager Paolo Di Canio during the summer, is likely to retain his place as the Black Cats attempt to return to Wembley in the FA Cup semi-finals.
They meet Hull for the third time this season on Sunday hoping for better fortunes that they have experienced in the two Barclays Premier League encounters, which has seen Sunderland lose on both occasions and lose a total of three men to red cards in the process.
Poyet has hinted he will make changes for the sixth-round tie as he attempts to manage the competing demands of a season during which top-flight survival is the overriding priority.
His side started the weekend sitting in 18th place in the table, one point adrift of safety with at least a game in hand on their closest rivals.
However, the 46-year-old knows that gap could have widened further by the time he sends his men out for what is a crucial home clash with Crystal Palace next weekend, and he admits he would rather have points on the board than extra games to play.
Poyet said: "The longer it goes and the more games we get in hand, it can be bad, it can be worse.
"There are teams who are winning and going away who were very close two or three weeks ago. If we or Everton go through, then it's another game that is going to be postponed, it's another game in hand, so you never get there and you don't know for real where you are.
"Again, we need to adapt. You can't have everything - if you are in the cup final, you are going to miss a game and if you are in a semi-final, you can miss another one, those are the fixtures.
"That's why I am trying to make sure we use the right team on Sunday because we will need everybody in the last few games. It's going to be incredible."