The Toon currently sit third, five points off second-place. But Given insists a fifth place would still be a great achievement with the Premier League's top five all qualifying for the Champions League nexy season.
Given told Tribalfootball.com: "No we're not looking at second place. I will say I'll take fifth now.
"On the 28th of April I will take fifth position. Look, they've got a really tough run in.
"It's Chelsea at home then they get Arsenal away, Everton home so it's not... it's the teams up there fighting for the top, I think they've got probably one of the toughest run-ins if I'm being brutally honest."
Reflecting on the Carabao Cup winners' Premier League campaign, Given was eager to remind critics how many were calling for the removal of manager Eddie Howe during their slump in November.
He continued: "That was probably the lowest sort of part of the season, wasn't it? And, you know, people were even questioning, some fans were questioning Eddie Howe at that point. It was ridiculous.
"Sometimes there's no middle ground. It kind of seems like you're going to win the league or you're going to get relegated. There's no sensible thoughts after a few bad results.
"You have to, sometimes in football, you have to take a step back and look at the bigger picture and look at what Eddie's done since he got in there and of course winning the Cup final now again has elevated him even higher in people's minds."
Newcastle must improve squad depth
Meanwhile, no matter where Newcastle finish on the table this season, Given expects a busy summer market.
The Irishman points out Newcastle have kept their chequebook relatively closed in recent transfer windows.
Given said, "To move the club forward, you have to strengthen again, there's no question because if you go back to last season, they had the Champions League campaign as well and what did jump off the page was the squad wasn't strong enough for the Premier League, Champions League, League Cup and FA Cup.
"So I think they need more strength in depth and they need again to move the club forward. They need more players of a high quality."
- Shay Given was speaking to Tribalfootball.com on behalf of CopyBet