Spurs pushed hard for a late winner in the afternoon heat at Stamford Bridge, with Gary Cahill clearing a second-half effort from Adebayor off the line, but were optimistic afterwards despite remaining winless in the league since February 11.
“I think it’s a step in the right direction after the results that we’ve been having. Hopefully we can take that forward now and push on,” Walker told Sky Sports.
“There’s eight games to go so it’s going to be difficult - we know that with the teams in the Premier League, it’s not easy going to places - but we’ve just got to keep believing in ourselves as a squad, as a team, and hopefully we’ll get to the top.
“I believe, with the people we’ve got in the changing room, we can destroy any team, so it’s just a matter of putting the trust in them and going to get the goals.”
When asked about the tactical battles which influenced a tepid first half, the right-back added: “Coming to Stamford Bridge, it’s always going to be ‘you have it, we’ll have it’ and ‘you keep the ball, we’ll have the ball’.
“I thought we did well as a team, we defended well.
"We were organised as a defensive back four, and a back five with Scotty [Parker] in there as well, so I’m pleased with the defending and the point.”
Adebayor, meanwhile, was disappointed not to have buried his chance when presented with an open goal but was encouraged by the overall showing.
“As a striker, as soon as you dribble [past] the keeper, you think you are going to score – that’s why I tried to take the ball as quickly as possible,” said the Togolese forward.
“But I think it was a great comeback from Cahill. I wish I could’ve scored but at the end of the day we got a point and we have to be pleased with that.
“It’s important the way we played today that we show character and personality, keep the ball very well and have a chance to kill the game, but it hasn’t happened for us again today.
"We just have to keep believing and keep doing our thing.
“It’s very important to keep a clean sheet and we are very pleased with that.
"Now we just have to keep the belief going and keep working hard in training every day, and we’ll see what we can achieve.
“Hopefully the luck will be on our side - you can see today that Gareth Bale hit the bar with a header.”
Spurs now prepare for their rearranged FA Cup quarter-final against Bolton on Tuesday, which had been abandoned at first attempt due to Fabrice Muamba’s on-pitch cardiac arrest.
How do you stay up to date with football when on the move? With http://m.goal.com – your best source for mobile coverage of the beautiful game.