With no further goals, the game went down to a shoot-out and Spurs eventually went out after Pascal Chimbonda missed in sudden death.
Defender Woodgate told five: "No-one likes to lose on penalties, it is not nice really - but we did not play well in the first leg.
"They did not have a chance in this game and we kept them busy but full credit to them, they got through on the night."
Tottenham won the Carling Cup earlier in the season but their European exit means they only have a top-half finish in the Premier League to focus on.
"We now want to try to push as far up the league as possible," Woodgate added.
