The Gers were hoping to pull clear of both Hearts and Aberdeen on Wednesday but they were left disappointed after a poor performance away from home.
Hearts' Robbie Muirhead scored a brace with his goals coming either side of half-time but Rangers did go close on two occasions. Joe Dodoo had a goal ruled out for offside and Joe Garner saw his effort cleared off the line, but Warburton was left frustrated.
Wednesday's result leaves Rangers in third, level on points with Hearts and just two in front of Saturday's opponents Aberdeen.
Warburton's men will play the Dons at home this weekend and the former Brentford coach has urged his squad to grab all three points, which punters can back using a free bet.
He told Sky Sports: "Any points you drop are valuable, the good thing is we get the chance to put it right on Saturday. We have to have a good response. There is no feeling sorry for yourself. We weren't good enough tonight and that is us as a group.
"Everything is together and tonight we have to recognise that, it is important sometimes. Honesty is the best policy, you can mask over it and say we should have had the offside goal and we had one cleared off the line - no.
"Tonight as a group of players we didn't think we were good enough and what we have to do is respond very positively and look forward to the game against Aberdeen."