A third minute free-kick from EFL Young Player of the Month Liam Mandeville was the difference at the Keepmoat Stadium, as Town went down to defeat in front of over 4,000 travelling Mariners.
Speaking after the game, Bignot said: ''I'm gutted for the players. They gave everything today and I believe that is Doncaster going top of the table and we've gone all the them all the way. I think if you ask Darren Ferguson, I think he's played the game and managed the game long enough to know they had to work very hard to earn those three points today.
''Listen, we've played two games and against two teams that should be going up automatic, if not play-offs and they've be disappointed with that, and what has settled the games is two free-kicks.
''I believe you look at the game in terms of getting into good goalscoring opportunities, I wouldn't say clear cut chances but they should've been chances. I believe, going off emotion and memory we edged getting into real good areas, whether that be around the 18-yard-box or in it and we shaded those chances too.
''It's that last little bit but for me, we tried everything today, we've used all the centre forwards we've got available to us and we put them on there and were positive and tried what we could do to get a positive result from this game.
Top scorer Omar Bogle missed the game with a thigh injury that he picked up in training, but fans will be pleased to hear that the injury won't keep Bogle out for too long.
Bignot said: ''An injury for Omar, he hasn't trained all week to be fair to be honest but came out yesterday and he came through it so we thought he'd be okay for today but obviously he had a reaction in the morning.
''He'll be fine, we've got a little break now of nine or ten games till the next game so fingers crossed he should be okay.''
Speaking of the support from the travelling Mariners faithful on the day, the Town manager said: ''Listen, they're a joke with the support they ring. What a club to play for and what a club to manage. I will give everything to this football club and I will expect the players to give everything for this football club and what you saw today is that they gave everything and just fell short.''
Town now face two home games before the New Year, starting with Accrington Stanley on Boxing Day, and Bignot is naturally hoping to get back to winning ways.
He said: ''At the end of the day, we can stand here and talk about this, that and the other but its results now.
''I'll take a crap performance and a scrappy 1-0 but certainly, winning football matches breeds confidence but they'll have a lot of positives to take from this run of games and we'll take them into the two home games.
''It's a great club to play for and I want those players to go out and express themselves in everything they do.''