Despite digging deep for large parts, the relegation-threatened visitors fell just short in the end and now face three crucial matches against Manchester United, Watford and Everton in their end-of-season run-in.
"I think our gameplan worked really well," BBC Sport quotes Neil as saying. "Petr Cech made three or four good saves. There was a five-minute spell when we were stretched and Arsenal managed to score in that spell.
"The last thing you can do down in the dogfight is feel sorry for yourselves. We didn't get what we deserved. We need three displays like that in the next three games.
"If you start worrying about the maths and what other people are doing then it'll drive you crazy. We have two games coming up and they will be key for us. We've got Manchester United and then Watford. We have to take maximum points from that."