England, eliminated at the group stage after a dismal performance in the World Cup four years ago, won by virtue of hitting more boundaries after the match, and a Super Over, both ended in ties.
"This has been a four-year journey, we have developed a lot. We find it hard to play on wickets like that and today was about getting over the line. Sport is tough at times," Morgan said.
New Zealand made 241 for eight after winning the toss and England were in trouble when they slumped to 86 for four.
But a 110-run fifth-wicket partnership between Ben Stokes and Jos Buttler gave the hosts a chance, and Stokes went on to make 84 not out as England were dismissed for 241 off the final ball of their 50 overs.
Stokes and Buttler returned to score 15 in England's Super Over before Jimmy Neesham and Martin Guptill made 15 for New Zealand, leaving England as the winners because they hit more boundaries in the match.
"There wasn't a lot in that game," Morgan said. "I'd like to commiserate with (New Zealand captain) Kane Williamson and his team. The fight they show is worth aspiring to, the example they set is commendable to all. It was a hard, hard game where people found it hard to score.
"We are delighted that we are lifting the trophy."
England lost to Pakistan, Sri Lanka and Australia in the group stage, putting their chances of reaching the semi-finals in jeopardy, but they beat India and New Zealand to make the last four before crushing Australia to get to the final.
"We had two must-win games and we scraped through and we continued it on to today," Morgan said.
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