Redknapp emerged from his opening fixture with a well-deserved point in a 0-0 draw at Sunderland. However, they will head into Saturday's home clash with Aston Villa still awaiting their first Barclays Premier League victory of the campaign and having collected just five points, remain rooted to the foot of the table.
Redknapp said: "It's going to be tough, we mustn't kid ourselves. You look at the position we are in - it's very, very difficult. But I can see there are some decent players there. We need to play as a team and be a team and if we can put them together and get them to work together, we have got a chance."
Rangers may not have collected that elusive first victory but they can leave the north east with their heads held high after a spirited performance. Home keeper Simon Mignolet managed to keep out first-half efforts from Djibril Cisse and Jamie Mackie and then a third from substitute Shaun Wright-Phillips late on.
However, they needed Julio Cesar and half-time replacement Rob Green to deny Steven Fletcher, the only man to really threaten to answer the pleas of the home fans to attack the side rooted to the foot of the table.
Redknapp has already been linked with a lengthening list of potential transfer targets with onlookers anticipating a January spending spree, but in the meantime, he is concentrating only on the players he inherited from predecessor Mark Hughes.
He said: "You can only work with what you have got, can't you? I can't pluck anyone out of the air at the moment. You can't bring anybody in, you have just got to get the best out of the players who are here."
Opposite number Martin O'Neill cut a disconsolate figure, saying: "It was a rather frustrating evening, I think frustration would sum it up. It was tough for us."
Cattermole, who shook off a knee injury to start, departed with just seven minutes played having damaged the other knee in a 50-50 challenge with Samba Diakite. And O'Neill added: "Losing Cattermole so early on in the game disrupted us somewhat, but even so, that's a handicap you have to overcome. It was just a frustrating evening."
Source: PA
Source: PA