Spurs needed a superb late winner courtesy of Gareth Bale to beat Saints 1-0 on Saturday, with the three points leaving them in fifth position in the Premier League.
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"We didn't play well in the first half, but we deserve [the three points] after what we did in the second half," he told the club's official website.
"We improved and Southampton closed the spaces, they gave us lots of difficulties, but we got what we deserved in the end. [It] was probably not about the performance. It was about getting the result.
"It was not the 'Spurs way', but in the end it keeps us in the frame and hopefully we will improve, and play better against Chelsea. It's a big, big game."
The north Londoners then face Stoke and Sunderland in their final two games, and the 35-year-old is targeting maximum points to keep up with their "improving" rivals.
"It will be extremely difficult, but if we achieve these nine points we will be enjoying Champions League football next season," he added.
"That is our aim, but we understand that other teams are improving and it will probably go down to the wire.
"The three points gives us a wonderful opportunity against a team that is fighting for the same objectives as us."