Willian made his mark after hitting the post twice in the second half but Andres Iniesta and Lionel Messi combined to capitalise on an Andreas Christensen mistake in the 74th minute.
Messi's goal leaves Chelsea needing a win or a high-scoring draw in the return leg in March and Alonso believes that his side have shown that they can get the job done against the Catalan giants.
"We have no fear," Alonso said. "We have important games now in the Premier League, we have to focus on that but then we have to prepare for this game well. We must try to play another good game there and see what happens.
"I think we controlled the game well. We defended very well and I am a bit disappointed to not take the victory, but we take away the positive stuff. We showed we can play and we can win against a big team like Barcelona.
"With the draw, it is disappointing. We did the perfect game apart from that mistake but it can happen to anyone. It has happened and now we have to think of the next game and not what has happened.
"We will have to take all the positive things and put in an extra shift in Barcelona because it will be even more difficult. But we definitely can do it and we will fight until the end."
Christensen began the season as a back-up option for David Luiz but he has forced his way into Chelsea's starting line up with a series of consistent performances since returning from a two-year loan spell at Borussia Monchengladbach.
Alonso has been impressed with his 21-year-old team-mate and he believes that he will not get too down about his mistake that gave Barcelona their away goal.
"He is okay," Alonso added. "It can happen to everyone in any game. We had to try to play because we can't just counterattack for 90 minutes and it is just a mistake.
"It has not been a very good season so far for Chelsea but it has been a good season for him.
"When we win, we win together; when we draw, we draw together.
"Now we have another tough match but it will be nice to play 90 minutes in Barcelona and Chelsea will give problems until the last minute, for sure."
Alonso had been out for three weeks ahead of the midweek clash, but he says that having made 34 appearances already this season, he was bound to pick up a small injury along the way.
"Just a couple of weeks out is not that bad after playing more than 30 games already," he continued. "I have been working hard to get back today and I am happy to help the team again. It wasn't a break, it was a little injury, but this can happen and it is good that I can recover very quickly and now I am ready for the next game."