The north London outfit found themselves 2-0 down in the first leg at White Hart Lane before Emmanuel Adebayor and Gylfi Sigurdsson helped rescue a draw.
And, though the Swiss side remain ahead on aggregate prior to the return fixture, Dawson is confident that Spurs can plot a route to the last four.
|BASEL PUT TO THE SWORD?
|14/1||Tottenham are 14/1 to beat Basel 2-0 with William Hill|
"So it's down to us and we're in a good position to go through, despite what some people think."
Tottenham need to win in Switzerland or draw by a scoreline of 3-3 or higher to go through on away goals against Basel, while in the Premier League they sit fourth in the table, level on points with Chelsea in third and two ahead of Arsenal but having played a game more than each of their nearest rivals.