The big-name free transfer from Chelsea was dismissed late in first-half injury time of his new club's season-opening 1-1 Barclays Premier League draw with Arsenal at Anfield.

Liverpool recovered from the setback to take the lead through David Ngog but were denied victory by a last-minute own goal from Jose Reina.

Hodgson said: "He is devastated - his debut at Liverpool, fantastic atmosphere, so desperate to do well.

"He was not playing at the top of his game, but was trying hard to get to that level, when suddenly he gets sent off.

"He was saddened by it all and not least because it put us in a difficult situation."

Cole was shown a straight red card for a reckless challenge on Laurent Koscielny.

Hodgson felt the verdict was harsh and the club are now considering whether to appeal.

Surprisingly, they could find a character witness in Arsenal manager Arsene Wenger, who expressed sympathy for the England midfielder.

Wenger said: "It was completely in the corner and I was on the bench, so I couldn't see it.

"But Joe Cole is usually a fair player, he is not one I would record is a guy who tries to hurt people. It is not his style.

"Maybe he was a bit rushing in his tackle.

"He kicked him - certainly accidentally - well because he [Koscielny] had a big knock on his shin.

"Fortunately his shinpad protected him well.

"We were scared it was broken because when he was moved off the pitch the physio told me it could be broken."

Koscielny, a £9.7million summer signing from Lorient, returned to the dressing room at half-time on a stretcher but was able to run out for the second half.

Koscielny was himself later sent off himself in injury time for a second bookable offence.

Hodgson added on the Cole incident: "Of course we now have the benefit of replays on the TV and those replays suggest to me he was a little bit unlucky.

"I don't think he dived to tackle the player, he dived in front of the ball to try to stop it being played down the line.

"The player got his legs caught up with him and maybe slightly twisted his knee.

"I was pleased to see there was no serious damage as he was able to play the second half."

Arsenal dominated possession in the first half but Liverpool threatened on the break and it was the Reds who upped the tempo after the restart.

Ngog scored a minute into the second period and the Reds had a number of other opportunities to increase their lead.

Arsenal finished the stronger and after Tomas Rosicky had forced a fine save from Reina, the Gunners broke through in the closing moments.

Reina looked to have claimed the ball after Marouane Chamakh's effort hit the post but it squirmed from his grasp and over the line.

Hodgson said: "I thought it was a fantastic effort but points are hard to come by in this league, so when you get so close you can't avoid that feeling of disappointment.

"Maybe that second-half performance deserved all three and not just one, but if someone had said at half-time you'll defend well and get a 0-0 or 1-1 I would probably have accepted that.

"But to lose it so close to the end to a rather scrappy goal was tough on us.

"He [Reina] took it hard because he is a very serious professional who really believes in himself and the team.

"There were an enormous number of positives but the unfortunate negative was that he let in a goal which under normal circumstances he would have kept out."

Wenger, whose side were without Cesc Fabregas due to sickness, felt his team deserved their point.

The Frenchman said: "They took the fluency, intelligently, out of the game.

"We just kept going and threw more and more people forward and in the end got, I believe, a deserved equaliser.

"I couldn't see us losing a game like that without being deeply hurt.

"We had a lot of possession and I agree we lacked a bit of spark in the final third, in combinations, in speed but overall we have shown the right attitude."