The Wasps came closest to a breakthrough after a dominant first-half, but Dario Zanatta’s drive 14 minutes from time crashed back off the crossbar.
“Prior to the game if you had offered me a 0-0 draw, a good point, I probably would have taken it,” said Goodwin, whose side move five points clear of bottom side Falkirk and to within a point of Partick Thistle. “But, on reflection of the 90 minutes, we were the better team.”
It was a familiar tale in the end for Inverness, who drew for the fifth game in succession and failed to find the net for the third time in that run.
“Alloa deserved to win the game, I make no bones about it. In the first-half, they could have been out of sight,” said manager John Robertson. “I’ve got to congratulate my players on keeping a clean sheet.”