The Republic of Ireland international expressed his views after watching Roman Pavlyuchenko score the only goal of the game in Saturday's 1-0 win against West Ham at White Hart Lane. The victory lifted Spurs to 41 points and within three points of the Hammers in the seventh position which should guarantee a place in the revamped Uefa Cup next term.
Keane feels a place in the Europa League could be attained which would cap a remarkable transformation in fortunes after Spurs started the season with two draws and six defeats.
"There is no reason why we can't," he said. "There is such a slim margin between relegation and seventh spot."
He added: "If we can kick on past the 40-point mark then next season we can push on.
"Harry has a great reputation. He's come in now and given the players belief."