Jesse Lingard gave United the lead on 61 minutes but Diego Costa's injury-time equaliser meant Louis van Gaal's side had to settle for a point.
"We played very good football," Mata told Sky Sports.
"Coming here to Chelsea isn’t easy, but particularly in the first 30 minutes and in the second half we played well – we had it so close.
READ MORE | Lingard: Draw feels like a defeat
Despite his annoyance, Mata said he was happy with United's recent form.
"When you win and when you play good football, confidence grows," he said. "I think we're showing now that we can play a high level of football and can play attractive, offensive football.
"That's what we're trying to do – that's what the fans want to see, so we try our best in every game. I think the last three or four games we've played really well."