Real Madrid held by Al-Hilal after Man City win Club World Cup opener
Federico Valverde had a stoppage-time penalty saved as Real were forced to settle for a point in the Group H match in Miami having earlier taken the lead.
It was a disappointing outcome for the large contingent of fans of the Spanish side in the impressive crowd of 62,415 at the Hard Rock Stadium.
"The first half wasn't as good as the second one. In the second half we had better chances, better control. For sure we have the principles to start building something but we could have won," Alonso told broadcaster DAZN.
The former Bayer Leverkusen coach gave debuts to new signings Trent Alexander-Arnold and Dean Huijsen in defence but Real were missing top scorer Kylian Mbappe for the game.
Gonzalo Garcia was brought into their attack as a result and the 21-year-old seized his chance as he opened the scoring just after the half-hour mark from a Rodrygo assist.
However, Al-Hilal hit back in their new coach Simone Inzaghi's first game on the bench with Ruben Neves levelling before the break from the penalty spot following a Raul Asencio foul.
Al-Hilal then held out for a point but Real had the chance to claim the victory in stoppage time after Mohammed Al Qahtani was ruled to have put his hand in the face of Fran Garcia in the box.
However, Valverde's spot-kick was saved by Yassine Bounou to give the Saudi team a draw after a hugely creditable performance.
Foden stars, Guardiola satisfied
In Philadelphia, Phil Foden and Jeremy Doku scored first-half goals as Pep Guardiola's City eased to a 2-0 win against Wydad Casablanca of Morocco in Group G.
City gave debuts to new signings Tijjani Reijnders and Rayan Cherki while it was Foden who opened the scoring inside two minutes, sweeping home inside the box after goalkeeper El Mehdi Benabid patted a Savinho centre into his path.
Doku converted the second goal from a Foden corner shortly before the interval in a game played in sweaty early afternoon conditions in front of 37,446 fans at Lincoln Financial Field.
The afternoon was slightly marred for City as Rico Lewis was sent off for a dangerous tackle late on, but Guardiola was satisfied with the winning start as his side look to turn the page following a difficult last season.
"It is so hot. The humidity is not easy. We had good moments, many new players. The first game in this group stage is always really, really important. I saw many, many good things," said Guardiola, who suggested he will make sweeping changes for the next match against Al Ain in Atlanta on Sunday.
"The first step is done, it is really important. Now we have recovery, we are going to train well in the next few days and then fresh legs for the next game to try to improve things," Guardiola added.
"We have a lot of new players, injured players back, and step by step we will get to the right tempo."
The action continues later on Wednesday as City's Group G rivals Al Ain and Juventus meet in Washington.
Before that, Mexican outfit Pachuca take on Red Bull Salzburg of Austria in Group H in Cincinnati.
The second round of group games begins on Thursday, with matches including Lionel Messi's Inter Miami against Porto and European champions Paris Saint-Germain facing Copa Libertadores winners Botafogo.