The Championship side's boss maintains his players can take heart from their performance at Wembley and is now concentrating on securing promotion to the Premier League
Kenny Dalglish's men required penalties to overcome the Championship outfit after the score ended at 2-2 after 30 minutes of extra time.
Steven Gerrard's cousin, Anthony Gerrard, missed Cardiff's crucial penalty in the shootout but Mackay is adamant his side showed their class at Wembley.
"I think today we were playing against a top team and I think we have got a lot to be proud of, you have seen two teams who have put everything into that game," Mackay told BBC Sport.
"We wanted to come here and win today but the players have done the club proud."
A Martin Skrtel goal cancelled out Joe Mason's strike and after an extra-time goal from Dirk Kuyt, Ben Turner netted in the 118th minute to ensure the tie went to penalties.
Mackay is now focused on securing promotion with Cardiff and maintains his side can maintain pride after reaching the final of the League Cup.
"Maybe if we had been beaten five or six, the question would have been valid, as it is, I don't think it is. We lost with dignity."
"We can take a lot of self-belief from getting to the final of a 92-club competition and taking a team at the top of the Premier League to penalties.
"We have 14 games to go and we are among 10 teams who can get into those play-off positions.
"We will patch up our squad and give it the best shot we have got from now until the end of the season."