Scotland skipper Preston Mommsen was frustrated not to have run England closer after the Saltires fell to a 119-run defeat in Christchurch.
He blamed a slow start for gifting their opponents an advantage they did not relinquish.
“Having won the toss, we’re very disappointed with the start we had with the ball,” he said.
“Second half of our innings I thought we did brilliantly, to restrict them to only 300 with the platform they had and the batters they had to come.
“We went into the half-time break, we were pretty confident we were in with a shout there. It was a good wicket, and unfortunately with the bat we just couldn’t quite get going.”
Scotland had hoped to claim a giant-killing, after running new Zealand far closer than England did in their opener.
“I think we’re a better side than what we showed there today,” Mommsen added.
“There were some things we didn’t do very well. There were some things we actually did very well.
“We couldn’t quite put in the full package, and that’s very disappointing, and that’s quite regrettable. But it just wasn’t meant to be today.”
England opener Moeen Ali’s second one-day international century ensured that any threat of a slip-up – in a match that loomed as a potential banana skin – was quickly averted and helped settle an England side shaken by heavy back-to-back defeats to start their tournament.
Captain Eoin Morgan said: “I don’t think there was ever a state of panic. We had two hard games and the fact we didn’t perform was disappointing.
“A win just puts things a little more at ease. It gives guys a little bit of confidence even the guys who didn’t perform today.
“Talking to guys who had a little bit of success today will be good for them.”
England’s first win at the tournament was built around Moeen’s 172-run opening partnership with Ian Bell.
The pair were hardly troubled as they broke the England opening partnership record at a World Cup – previously set at 158 by Dennis Amiss and Barry Wood in 1975.
Scotland barely managed to better that in their reply, as they were bowled out for 184 in 42.2 overs and, after Moeen claimed two wickets to go with his 128 from 107 balls, Morgan revealed he felt “privileged” to be able to call on his match-winning potential.
“I rate him really highly. He’s an all-rounder that we haven’t had for a very long time,” he said.
“He’s somebody who opens the batting and plays in the fashion that he does and the purchase he gets on the ball. I think we are very privileged to have him.
“We certainly don’t undervalue him.”
England’s next move is to return to the scene of their humiliation at the hands of New Zealand with their next match against Sri Lanka in Wellington on Sunday.
They will fly back to the New Zealand capital with a greater deal more confidence, albeit having beaten a Scotland side still searching for a first-ever World Cup win, after sticking with the same team that were blitzed by the Black Caps.
“We obviously considered it (making changes),” Morgan said.
“We came to the conclusion that we haven’t performed in the first two games so to argue the balance of the side was wrong, you couldn’t really do it because we hadn’t seen guys perform.
“I was very confident going into the first two games that we had the strongest side to win those games so by reinforcing that confidence with going in with the same team today was very important.”
Steven Finn suffered a mauling at the hands of Brendon McCullum in Wellington, his two overs cost a remarkable 49 runs, but rewarded the faith kept in him with three for 26 from nine overs.
Morgan also enjoyed a profitable day, hitting 46 from 42 balls, to suggest his run of outs were behind him.
“There were a lot of positives to take from today,” he said.
“Moeen and Finny were brilliant and there were guys around that. Guys building around match-winners is a good sign.”
Morgan’s innings began as a slow burner, taking 10 balls to get off the mark as England lost direction around the batting powerplay.
England lost three for two at one stage but the skipper timed his late hitting precisely to drag the score beyond 300.
“It’s nice to spend a bit of time at the wicket and get some runs given my run of low scores,” he said.
“It’s not easy to come in and bang it from ball one. It was a bit more of a calculated and reserved innings today.”