Although Ellis Simms put the visitors 1-0 ahead in the opening minutes, Daizen Maeda, Kyogo Furuhashi, Matt O’Riley and Giorgos Giakoumakis struck in what finished as a convincing Celtic win to all but secure the Premiership title.
“I’m disappointed with the final outcome,” said Neilson. “We started the game very well and, although Celtic put a bit of possession together, I thought we were comfortable in the areas we were keeping it. Then the first goal rocked us a bit and the second took it away from us.
“We came out second half at 2-1 and then we gave away a third at 65 minutes when we had been coming back in the game again, so I think it is just giving away goals at key moments.
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“Towards the end Celtic bring on five attacking players and that takes the game away from us. That is the difficulty we have, we have to build a squad that come here and they make five changes that can really influence the game.
“Today, we had maybe two changes we could make. That is the difference. They are a very, very good team and they can make the changes.
“We are not going to get a £50 million transfer budget so you try and just take steps every time, try and build a team that come here and challenge.
“There is a reason they are so many points clear. Their starting 11 is great and then they can make changes which gives them another gear. We just have to get closer and closer.”
Hearts were upset with referee Don Robertson at Celtic’s first goal as Callum McGregor appeared to foul Toby Sibbick seconds before Maeda equalised.
“It is a free-kick, to be honest,” stressed Neilson. “I have seen it again and am pretty sure you will agree. These key decisions when you come here, you have got to get them. That was the disappointment with the ref.
“I thought it was a pretty simple one to get and he doesn’t get it right. The second one for the goal [when the ball narrowly crossed the line] is the right decision – borderline but right.
“Those two goals, one he has got right, one he has got wrong and that is the difference. So I am frustrated about the first goal, yes. It is not worth [speaking to the officials]. Don was the same at Easter Road so I will just keep my mouth shut. We have a big game coming up in a couple of weeks time.
“I think there was a lot of positives, though. We started well, came out for the second half and knew if we could get to 55-60 minutes we would start getting into the game again so the actual gameplan was good. Celtic bring on five international players up front it is going to take the game away from you.”