The 46-year-old Uruguayan has enjoyed a measure of success since replacing Paolo Di Canio at the helm in September, and has increased the club's meagre points total from one to eight during the ensuing weeks.
Performance levels have increased significantly too and the Black Cats emerged from Wednesday night's 4-3 defeat by title-chasing Chelsea with their heads held high.
However, they did so empty-handed and will embark upon Saturday evening's home clash with Tottenham still sitting at the bottom of the Barclays Premier League table and eight points adrift of safety.
That is a situation Poyet knows has to change sooner rather than later if they are to maintain their top-flight status.
He said: "Unfortunately, we still don't have enough points, we still look at the table and it's not great. We need to win football games.
"That balance is slightly going one way. We need to start maybe taking a few more risks because we don't have enough points.
"We are in a situation where it is difficult to catch the teams in front of us because we cannot put two wins together. Every time we make a step forward, the second step is flat or backwards and we cannot really get there.
"The league is like that - everybody beats everybody, every game is difficult. All the teams are going to win football games and we haven't won enough."
Despite their plight, Poyet has seen enough both on the training pitch and in games to believe his squad is equipped to mount a fightback.
He said as much after the Chelsea game and had his view endorsed by opposite number Jose Mourinho after the final whistle.
Asked what the Portuguese had said in the wake of the seven-goal thriller, Poyet revealed: "In different language, he said more or less the same: 'If you play like that, you won't go down'.
"It's good that the players can see that as well because it is a compliment to the players.
"For me, if we play seven or eight games like the other day and against Aston Villa and we don't win one, there is something that's incredible against this football club.
"But it doesn't happen. If we perform like that for seven or eight games, you are going to win three or four, so that's what I am looking for.
"I am looking forward to seeing if we can maintain that and find that balance.
"We defended very, very well against Villa; we didn't score from two yards. We scored three against Chelsea and you should win, and we conceded four and we defended really badly.
"Football is a complete game: you need to defend well and score your chances, and then you become a consistent team."
Striker Jozy Altidore is likely to retain his place as Poyet's lone striker for the clash with another of the manager's former clubs after getting the nod over Scotland international Steven Fletcher in midweek.
The United States frontman rewarded Poyet's faith in him with the opening goal, his first for the club in the league.
The manager said: "I am sure that a few of them (the fans) were not happy with me before the game, and then they say, 'Maybe he was right'.
"For decision to go right, you need the player. I can make 100 decisions, but it's up to the player then to make that decision right.
"He needed to play, it was the time I needed to make a decision. He didn't play in the previous two or three and I thought it was the right game for him. I am happy that I was right."