The Primera Liga leaders have had their advantage over Real Madrid halved to six points since mid-February and Gudjohnsen said coach Pep Guardiola and his side were fully expecting to be pushed all the way by the champions.
"To win titles you have to suffer right down to the wire," the Iceland international said on Barca's website.
"There are people who think we are playing better than Real but the team who play the best football do not always win."
With 11 matches left, Barca have 66 points ahead of their home match against sixth-placed Malaga on Sunday.
Real play Almeria earlier at the Bernabeu having won 11 and drawn one of their last 12 league matches since losing to Barca at the Nou Camp in December.
Captain Raul acknowledged that Real were relying on their arch rivals slipping up but insisted there was still a decent chance for the club to claim a third successive title.
"If Barcelona continue to play at their current level all we'll have left to do at the end of the season is congratulate them," the striker said on the club's website (www.realmadrid.com).
"But they have to come and play here (at the Bernabeu) and if they wobble before then we will be a little bit closer."
FINANCIAL WOES
Struggling Valencia have been energetically celebrating the club's 90th birthday this week but are looking for a first league win since the start of February when they play at in-form Racing Santander on Sunday.
Unai Emery's side have slipped out of the European qualification places into eighth and their problems on the pitch have been compounded by financial woes that have halted some payments to players and work on a new stadium.
Midfielder Ruben Baraja urged his colleagues to give their all for the rest of the season to help the club end its poor run and achieve the goal of qualifying for a lucrative spot in next season's Champions League.
"The most important thing is to forget everything that's going on around the team and focus on work and the matches that remain," he said on the club's website.
In Saturday's two matches, third-placed Sevilla are looking to cut the nine-point gap on Real when they host Real Valladolid and Villarreal, six points behind the Andalusians in fourth, entertain Athletic Bilbao.
