Sir Ian McGeechan praised his players despite Bath suffering a Heineken Cup home defeat against holders Leinster that has left them facing an early European exit.
Ireland fly-half Jonathan Sexton kicked six penalties - two during the last seven minutes - to give Pool Three leaders Leinster a tense 18-13 triumph.
The minimum requirement for Bath to now make the quarter-finals will be victory over Leinster in next Saturday's Aviva Stadium return, but rugby director McGeechan said: "I am very proud of the players - their attitude was superb. We defended tremendously well, restricting them to penalties, and it is about the small margins."
He added: "We made one or two errors. They got the ball into the right areas quickly and put the pressure on. They kicked the penalties.
"We probably didn't have quite that same amount of extended pressure, but we scored a very well-executed try, and that showed the attitude was really positive.
"The work-rate when we didn't have the ball was superb, and our attacking play was very encouraging. We just need to have a bit of composure at key times, but it is a relatively new team with new combinations, and that is what you grow towards.
"I think it took Leinster probably three or four years to get to that point. You don't get there overnight.
"Leinster have got huge experience and they have got good players in key positions. When you win European Cups, that's what you get. You know how to do it, you've been there before, and so it grows.
"They bided their time very well, and that is experience. That is a good team with good players reading the situation well."