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The Bulls were swept aside in a clinical first-half display by the National League North leaders, but showed far more intent after the break and were rewarded with a late Harrison Sohna goal.
And while the result ended Hereford’s recent winning run, Downes took encouragement from the attitude his players showed in trying to get back into the contest.
"I'd much rather lose a game 4-1, giving it a go, getting after them, and maybe exposing ourselves a little bit potentially, than just sitting back and losing 2-0 and not even throwing a punch," he said.
"We did that tonight, threw a lot of punches. We copped a couple as well, don't get me wrong, but that's a good side we played against tonight.
"I'm proud of the boys for the way they went about it."
Hereford made six changes with a demanding run of fixtures in mind, and Downes insisted he had full belief in the players he selected.
"I started a team that I felt was capable to go and win the football match, that was my intention, and that was the boys' intentions," he told the media at Edgar Street on Tuesday evening.
"I believe in all the players that we're playing. Felt it was right time to make a couple changes and shake up.
"There'll be more changes against Alfreton from the team that started tonight. But that's the nature of the beast when you're playing two games in two days."
The Bulls showed greater energy after the interval, with Sohna, Mikey Lane and Justin Donawa all going close before eventually finding a late breakthrough.
Downes also praised the supporters, who continued to back the team throughout despite the scoreline.