The Hammers extended their unbeaten run in the league to four matches on Saturday, with a point at White Hart Lane crucial in ensuring they stayed out of the bottom three.
We are staying up: Keane insists West Ham can maintain their Premier League status
It was also the first time they had kept back-to-back clean sheets for more than a year, something which has boosted the belief of Avram Grant's men ahead of their clash with Manchester United on Saturday week.
On-loan Tottenham striker Keane told his club's official website: 'I think, as a group of players, we certainly believe we won't get relegated.
'I think we have to believe that after a defensive performance like that and that we certainly have the players in the team who can score goals.
'The table is so close, so if we get a couple of back-to-back wins, we're right back up there again.'
On target: The on-loan West Ham striker has scored just once since his January move
Keane's hopes of helping West Ham's survival battle were hit by a calf injury that kept him out for more than a month.
The 30-year-old, who scored on his debut in February, returned for the recent FA Cup defeat at Stoke but was prevented from featuring on Saturday due to the terms of his loan agreement from Spurs.
He said: 'I'm looking forward to my future at West Ham. 'It's obviously been a little bit frustrating.
'I came back and unfortunately I got injured in my second game, which was disappointing, but luckily enough I'm back fit now and I played 20 minutes against Stoke and 65 minutes in the reserves.'
Keane, who should further boost his match fitness in two games for the Republic of Ireland in the coming week, added: 'The international games have come at a nice time for me.
'I'm looking forward to playing two games and hopefully getting myself back in the mix again.'
Those matches are immediately followed by the United match and Keane said: 'Manchester United is another tough game.
'Our home record is decent and we always do well against the so-called bigger teams so it's a game I'm certainly looking forward to and I'm sure the lads are too.'
?Robbie's Keane to vent frustration on Macedonia with Repubic of IrelandTottenham v WEST HAM: Keane unavailable as Hammers seek rare White Hart Lane winKeane reveals injury frustration as West Ham striker targets games - and goals?Explore more:People: Robbie Keane Places: Republic of Ireland
Source: Daily Mail
Source: Daily Mail