'We just need to keep going, get this season out of the way, stay up then concentrate on improving next season when we will be bigger and stronger,' said Keane, who has now scored two goals following his return to White Hart Lane from Liverpool.
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'When I was away from the club the results were disappointing to see how they were doing early on. I had a lot of friends at the club and still do. I was always looking for their result, but just look at the other teams that are down there.
'There are loads of them and there are some really big teams that can easily get relegated like Newcastle. The only ones that are safe are from Manchester United down to Everton. They are safe but no one else is. It is a strange league and it is good, but only if we stay up.
'It is tight at the bottom and we need the points badly but if we keep performing like we did against Sunderland we will be OK. There have been some quality players added since I left and Wilson Palacios has added some real steel in midfield. Maybe it is better now than when I left.
'We can't get too carried away. It would be difficult to take with a squad like this if we did go down but there is still a long way to go. Harry said the other day there could be up to 12 teams involved."
Tottenham will head to Champions League-chasing Aston Villa this Saturday buoyed by their late recovery at Sunderland that stretched their unbeaten run to three games.
Keane said: 'It was a very important result for us and if it had gone the other way it would have been difficult to take for us.
'It is important to take points against the teams around us. We are very close to Sunderland so it was vital to keep the points ticking over. The important thing was not to lose and we deserved to get something out of the game. It would have been a travesty if we had lost.
'It was a better point for us than for them because we scored in the last minute. There was a lot of pride out there. We had a lot of chances and we were getting frustrated because we knew they were there for the taking. It will help our confidence because we got something.
'We dominated it and we did enough to win the game. We went a goal down early on and we were chasing the game, but we stuck at it, kept plugging away and got back right at the end. We had a few chances and fortunately we managed to get the equaliser.'
Keane saluted those players who dug out a point following a spell of three games in seven days.
'You have just got to look at the fitness of the lads especially after the Carling Cup final,' Keane added.
'I didn't play in that game but it has been a long month for me because it seems I have been playing every day. I am just a person who loves to play all the time.
'Everyone did well against Manchester United in the Carling Cup and the energy they showed there was great as it was against Middlesbrough when we won 4-0. The winning mentality was superb as well. We look strong and fit and we got our rewards in the end.'