Spurs have been embroiled in a relegation battle all season but have now moved to 11th, their highest position to date, following a 2-1 victory at Aston Villa.
Tottenham are currently six points clear of the drop zone and just five behind seventh-placed West Ham.
The side finishing seventh is expected to secure a place in the revamped UEFA Europa League and Woodgate feels Tottenham can approach the rest of the season with confidence.
"Winning at Aston Villa was a big result for us, but I would rather be optimistic rather than pessimistic," the defender said in the Daily Express.
"I'd rather look up than down, try to win as many games as we can.
"We are on a good run. Europe? We have a chance but let's not get carried away.
"We have got a lot of work to do still, a lot of teams to play around us as well, so hopefully we can get involved in it."
Palacios praiseSpurs have enjoyed a good run of form since Wilson Palacios arrived at White Hart Lane from Wigan and Woodagte has been impressed by the Honduran midfielder.
Palacios has forged a good partnership with Jermaine Jenas in the centre and Woodgate feels they have made Tottenham harder to beat.
"We are more resilient," he insisted.
"We graft and we have two midfielders in Wilson Palacios and Jermaine Jenas who work hard. That has got to be a telling factor, particularly in our away games.
"That is what the manager demands. In a football side you have to do all the ugly things before you start playing with the ball.
"Palacios is proving his worth. He has been a good signing for us."