He admitted feeling for supporters after the 4-3 penalty-shootout loss but insisted the motivation within his squad is clear for all to see.
“I am just disappointed we couldn’t win it although I believe we gave the fans something to shout about because it has been a tough year for everyone,” said Neilson. “The fans can see now we have a group who are fighting and giving everything for the club.”
A gutsy Hearts performance earned plenty of plaudits even though Celtic prevailed to secure a quadruple treble.
Ryan Christie and an Odsonne Edouard penalty put the Glasgow club 2-0 ahead before Liam Boyce and Stephen Kingsley levelled the scoreline.
In extra-time, Celtic substitute Leigh Griffiths made it 3-2 but Josh Ginnelly’s equaliser took an enthralling final to penalties.
The Celtic goalkeeper Conor Hazard saved from Kingsley and Craig Wighton after Steven Naismith, Michael Smith and Olly Lee converted their spot-kicks.
Griffiths and Callum McGregor scored for Celtic before Craig Gordon saved from Christie. Mikey Johnston and Kris Ajer put Celtic’s last two penalties into the net.
As a second-tier club after their controversial relegation, Hearts were huge underdogs for the final. They matched Celtic every step of the way and were devastated at the end.
"The main feeling is pride,” said Neilson. “I am obviously disappointed with the result, but proud of the players and the performance they put in.
“The first half we were 2-0 down but in the second half I thought we were the better team, even into extra time. We went again and that showed the strength of the group.
Kingsley and Wighton were aghast seeing their spot-kicks were saved. “They are hurt and disappointed. They will feel it more and that is only natural,” added the manager.
“I have spoken to the boys already and the most important thing is that they stepped forward to take the penalties. If you have the bollocks to take a penalty in the Scottish Cup, that is all the matters to me.
“It is irrelevant if they miss, at least they stood up and took one. Now we all have to use this disappointment to win us the league and to make sure we are celebrating at the start of the season. We spoke about using this for motivation again. We have a league to win to get back into the top-flight.
“Our relegation has brought a togetherness because these boys have been in the trenches and want to take this team forward. There is a pride with what these boys left out there.”
Explaining his gameplan, Neilson added: “We set-up to give Celtic possession. We knew they would move it from side-to-side. We looked at Celtic over the last 14 or 15 games and the only teams they have beaten are teams who play three at the back, apart from AC Milan.
“We knew if we played with three we could make it very difficult for them and it would shut off all the areas for Christie and Elynoussoui. We gave up possession and it worked apart from a wonder strike and a penalty. They only had one other shot on target.”