A double from forward Robbie Muirhead, his first two goals for Hearts since signing in the summer, lifted the Edinburgh side above the visitors and into second place in the Ladbrokes Premiership.
Warburton was far from happy with the performance but has quickly turned his attention to the weekend clash with Aberdeen and is demanding his players bounce back quickly.
"Any points you drop are valuable, the good thing is we get the chance to put it right on Saturday," he said. "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."