The Black Cats have won three and lost three of their six games since the Uruguayan took charge in early October.
But Poyet knows the importance of building a good run of form and is hoping for a first away victory of the campaign against Aston Villa on Saturday.
|4/5||Sunderland are 4/5 with Bet365 to be relegated this season|
"If we keep believing in what we're doing I'm sure we will start picking up points away from home," he said. "The sooner we win a game the better for us and we have a great opportunity on Saturday."
Sunderland fell to a 2-0 defeat at Stoke City last weekend and Poyet took a philosophical view of the encounter, which saw Wes Brown wrongly sent off before having his red card rescinded.
"It depends how you take it – as a step back because we didn't win, or we could realise that even with 10 men we were competitive and had a chance to take something from the game," he continued.
"We'll see. I think the next game is important, to see the reaction.
"They [Villa] are a very difficult team to play against.
"They have options, they can change their system and they play with power, speed and youth.
"We need to be spot on. You need to be at your best in practically every game in this league, but this match in particular is going to be a big test for us."
And Poyet concluded that Sunderland would need to improve heading into a busy Christmas schedule.
"The run of consecutive games is so quick that if we put a good run of results together we can at least show the top of our heads out of the bottom three places," he said.
"It's going to be tough. It's not an easy run and there are plenty of important games coming up. The team is getting better and we need to believe."