"We are not going to finish [the season] unbeaten, it is impossible," Guardiola said. "But to fight to avoid that, mentally, and in the way we want to play, is fantastic."
Arsenal needed a spot kick in added time to secure all the points against Burnley and move to fourth.
Sanchez found the bottom corner two minutes into stoppage time after James Tarkowski was adjudged to have pushed Aaron Ramsey.
"Football's a harsh game and sometimes it hurts you," Burnley manager Sean Dyche said.
Everton are swiftly falling into a fight for survival after being thumped by Southampton.
Gylfi Sigurdsson's long-range strike cancelled out Dusan Tadic's opener, but Charlie Austin scored two second-half headers before Steven Davis rounded off the scoring.
Everton are 16th, just two points clear of the relegation zone.
Harry Kane admits Tottenham must turn around their stuttering form at Wembley after they were held 1-all by managerless West Brom.
West Brom secured a surprise draw when Salomon Rondon gave them an early lead before Kane equalised with 16 minutes left.
"It's hard to say why there was a slow start but it's something we're going to have to work on and try to change because these are games we have to be winning."
- AAP
