Albion, who have not won a league match on their travels since March 2014, found themselves 25-0 down to a powerful Ionians side, who dominated the set pieces.
But in the final quarter of the game, Albion scored three tries – one with the last play of the game – to only end up losing 25-21.
“It was a tough day,” said Dawe. “But we adapted in the end and full credit to the guys they hung in and came away with a point.
“There is spirit in the camp.
“We showed endeavour, we showed skill and I thought we deserved a bonus point for that endeavour and never-say-die attitude.”
Dawe, who was without injured forwards Dan Collier, James Penman and David Fisher, added: “We had a fair bit of play first half, but we didn’t always challenge their 22 enough.
“We had field position and ball, but we made some errors and didn’t get the scoreboard ticking early enough.”
The Albion boss was not happy with a number of the refereeing decisions, particularly at the breakdowns and scrums.
“I certainly don’t think we deserved to succumb to two penalty tries,” he said.
“Although we did have a high penalty count we handled the situation as best we could. You don’t expect any different playing away from home.”
Dawe remains confident his pack can cope in National One. As well as the injured Penman, Collier and Fisher to come back in, Dawe also now has new signing Gregory Sebastien, who was not included at the weekend having only arrived at the club on Thursday.
“We’ve coped admirably well in the first two games,” said Dawe.
When asked about the start to the season which has seen Albion pick up one win and two losing bonus point from their opening three matches against Richmond, Rosslyn Park and Hull, Dawe said: “We are competitive. It’s not ideal, but it is what it is.”
Dawe is waiting to find out the extent of the lower leg injury suffered to winger Robin Wedlake, which forced him off after 13 minutes.
“We are not quite sure what it is yet,” said the Albion boss. “It was a blow to lose him and he is a devastating rugby player on the ball.”